Why faster than light is impossible?

[scope]

hi,
could you tell me why traveling faster than light is impossible?
thank you!

 

[Skaffen]

As your speed increases so does your mass (more energy, more mass). As you approach the speed of light you require increasingly more power to keep accelerating...makes it difficult to get close beyond objects with a small mass like protons & ions. Impossible to get there with any rest mass, fortunately photons have no rest mass.

 

[Dale]

You are always at rest in your own frame, by definition. Therefore your four-velocity is timelike in all reference frames, which implies that your speed is less than c in all reference frames.

 

[Dickfore]

The Second Postulate of the Theory of Relativity tells us that there is a limiting speed with which interactions can propagate in Nature.

It is a consequence of this Postulate that no physical object can travel faster than this speed, since one can invent possibilities where particles are transmitters of force between other particles.

When one develops SR, it is shown that this limiting speed is not only impossible to overcome, but it is also impossible for any physical object to ever reach it, as it would require an infinite amount of kinetic energy to reach it. For physical objects with zero rest mass, however, it is the only possible speed with which they can travel.

It turns out, as well, that the speed of propagation of electromagnetic fields in vacuum is equal to this limiting speed. As light is an electromagnetic wave, this limiting speed is most commonly referred to as the speed of light in vacuum.

 

[bcrowell]

FAQ: Why can't anything go faster than the speed of light?

In flat spacetime, velocities greater than c lead to violations of causality: observer 1 says that event A caused event B, but observer 2, in a different state of motion, says that B caused A. Since violation of causality can produce paradoxes, we suspect that cause and effect can't be propagated at velocities greater than c in flat spacetime. Special relativity is one of the most precisely and extensively verified theories in physics, and in particular no violation of this speed limit for cause and effect has ever been detected -- not by radiation, material particles, or any other method of transmitting information, such as quantum entanglement. Particle accelerators routinely accelerate protons to energies of 1 TeV, where their velocity is 0.9999996c, and the results are exactly as predicted by general relativity: as the velocity approaches c, a given force produces less and less acceleration, so that the protons never exceed c.

The corresponding speed limit in curved spacetime is far from being established. The argument from causality is not watertight. General relativity has spacetimes, such as the Godel solution, that are valid solutions of the field equations, and that violate causality. Hawking's chronology protection conjecture says that this kind of causality violation can't arise from realistic conditions in our universe -- but that's all it is, a conjecture. Nobody has proved it. In fact, there is a major current research program that consists of nothing more than trying to *define* rigorously what the chronology protection conjecture means.

There are certain things we *can* say about faster-than-light (FTL) motion, based on the fundamental structure of general relativity. It would definitely be equivalent to time travel, so any science fiction that has routine FTL without routine time travel is just plain wrong. It would probably require the existence of exotic matter, which probably doesn't exist. If it were possible to produce FTL artificially, it would certainly require the manipulation of godlike amounts of matter and energy -- so great that it is unlikely that beings able to carry it out would have anything like ordinary human concerns.

There are many ways that velocities greater than c can appear in relativity without violating any of the above considerations. For example, one can point a laser at the moon and sweep it across, so that the spot moves at a speed greater than c, but that doesn't mean that cause and effect are being propagated at greater than c. Other examples of this kind include a pair of cosmic-sized scissors cutting through a gigantic piece of paper at greater than c; phase velocities greater than c; and distant, observable galaxies receding from us at greater than c, which can be interpreted as an effect in which space itself is expanding in the space in between.

 

[ghwellsjr]

It turns out, as well, that the speed of propagation of electromagnetic fields in vacuum is equal to this limiting speed. As light is an electromagnetic wave, this limiting speed is most commonly referred to as the speed of light in vacuum.

I think this is the relevant factor in answering the question why we can't travel or make things travel faster than light. Once you realize that light is an "extension" of matter, specifically charged particles (electrons), and that the electromagnetic fields surrounding matter is the mechanism that causes interactions between matter separated by local distances, then it is easy to see why we cannot exceed the speed of light. Our mechanism to "push" is essentially light itself and if it has a speed limit then we won't be able to use it to "push" something faster than it, itself, can go.

 

[scope]

ok, thank you then I am still worried with the spin of the electron. i know that it is widely believed that an electron is a point particle and its spin has not really the classical meaning.

but IF we suppose that its spin is really its proper angular momentum and IF we suppose that's its radius is very small but not 0, then I know that in classical physics, L=mvr leads to v>c.

but let's suppose the same conditions but let's do the calculation in special relativity. the electron is not moving at relativistic speed relativitely to us (at rest), and let's then suppose that gamma is 1 in the direction of its motion
then L=r.p and r is classical, and p=mv.
then I do believe that m is the same as the rest mass, and therefore the calculation in special relativity leads also to v>c.
is that calculation mathematically correct? i am just asking if that is mathematically correct?.

the problem is that its mass m is not a relativistic mass , it is a rest mass, so i wonder if the calculation in classical mechanics leads to the same result as in special relativity, mathematically?

 

[jambaugh]

ok, thank you then I am still worried with the spin of the electron. i know that it is widely believed that an electron is a point particle and its spin has not really the classical meaning.

but IF we suppose that its spin is really its proper angular momentum and IF we suppose that's its radius is very small but not 0, then I know that in classical physics, L=mvr leads to v>c.

but let's suppose the same conditions but let's do the calculation in special relativity. the electron is not moving at relativistic speed relativitely to us (at rest), and let's then suppose that gamma is 1 in the direction of its motion
then L=r.p and r is classical, and p=mv.
then I do believe that m is the same as the rest mass, and therefore the calculation in special relativity leads also to v>c.
is that calculation mathematically correct? i am just asking if that is mathematically correct?.

the problem is that its mass m is not a relativistic mass , it is a rest mass, so i wonder if the calculation in classical mechanics leads to the same result as in special relativity, mathematically?

Your formula assumes all the mass is at the same radius which implies a ring or cylinder shape...but that's just a matter of a multiplicative form factor. W.r.t whether the relativistic and non-relativistic calculations agree, they do. If we imagine an electron as a little spinning ring of mass then the mass we measure for the electron is the relativistic mass given the velocity of the rotation and that also is the mass one uses in the relativistic angular momentum via L=m v r = m omega r^2.

But let's try it this way. Take a loop of mass m and spin it to some fixed angular momentum. Then measure its tangential velocity v and total ("relativistic") mass M. The mass M will be rest mass times the relativistic factor and the angular momentum will be fixed L = M v r. Now shrink r and you will see the loop speed up. Note this takes some energy because you are increasing the total energy and so the relativistic mass will increase:
L = M v r = M' v' r'. You will find as you try to spin it past v=c by reducing r that you again hit that M->infinity business.

Note another aspect of the electron. There is energy tied up in the surrounding electromagnetic field. This contributes to the observed mass. If you try to concentrate the finite charge to small enough radius you will again get infinite energy and thus infinite mass.
What it more there is also an angular momentum component possible for that surrounding electromagnetic field.

You can from a classical perspective think of the electron as nothing except a charge monopole whose mass comes wholly from the EM field surrounding it, and avoid the infinite mass for a point charge by assuming a masking effect of the vacuum (the vacuum polarizes so as to spread the charge around.)

This goes to show that it is not correct to think of an electron as a point mass/charge except relative to a larger scale.

 

[bcrowell]

Our mechanism to "push" is essentially light itself and if it has a speed limit then we won't be able to use it to "push" something faster than it, itself, can go.

By this logic, a rocket wouldn't be able to accelerate to a speed greater than its own exhaust velocity. Hand-waving arguments like this don't prove anything.

 

[bcrowell]

ok, thank you then I am still worried with the spin of the electron. i know that it is widely believed that an electron is a point particle and its spin has not really the classical meaning.

but IF we suppose that its spin is really its proper angular momentum and IF we suppose that's its radius is very small but not 0, then I know that in classical physics, L=mvr leads to v>c.

It's not just that it's "widely believed" that its spin is nonclassical. It's mathematically impossible for a spin of \hbar/2 to result from motion of a particle through space. You can only get integer multiples of \hbar that way.

 

[scope]

Your formula assumes all the mass is at the same radius which implies a ring or cylinder shape...but that's just a matter of a multiplicative form factor. W.r.t whether the relativistic and non-relativistic calculations agree, they do. If we imagine an electron as a little spinning ring of mass then the mass we measure for the electron is the relativistic mass given the velocity of the rotation and that also is the mass one uses in the relativistic angular momentum via L=m v r = m omega r^2.

But let's try it this way. Take a loop of mass m and spin it to some fixed angular momentum. Then measure its tangential velocity v and total ("relativistic") mass M. The mass M will be rest mass times the relativistic factor and the angular momentum will be fixed L = M v r. Now shrink r and you will see the loop speed up. Note this takes some energy because you are increasing the total energy and so the relativistic mass will increase:
L = M v r = M' v' r'. You will find as you try to spin it past v=c by reducing r that you again hit that M->infinity business.

Note another aspect of the electron. There is energy tied up in the surrounding electromagnetic field. This contributes to the observed mass. If you try to concentrate the finite charge to small enough radius you will again get infinite energy and thus infinite mass.
What it more there is also an angular momentum component possible for that surrounding electromagnetic field.

You can from a classical perspective think of the electron as nothing except a charge monopole whose mass comes wholly from the EM field surrounding it, and avoid the infinite mass for a point charge by assuming a masking effect of the vacuum (the vacuum polarizes so as to spread the charge around.)

This goes to show that it is not correct to think of an electron as a point mass/charge except relative to a larger scale.

thank you, but I thought that not only the relativistic mass is changed, but also the velocity, because the momentum mv is a 4-vector,
so shouldn't be the formula L=mvr/gamma instead of mvr.gamma?

 

[ghwellsjr]

By this logic, a rocket wouldn't be able to accelerate to a speed greater than its own exhaust velocity. Hand-waving arguments like this don't prove anything.

What if I said, by your logic, a rocket could exceed the velocity of light?

Please try to understand how I'm trying to help someone who asks, "why can't we go faster than the speed of light?"

If you don't keep changing your reference frame but analyze the situation from a single reference frame, and you understand that even rockets with exhaust are dependent on the interactions between charges and their surrounding electromagnetic fields which they create and which propagate at the speed of light and which then interact with other charges to make them move, then maybe you will understand what I'm trying to communicate. I realize that it is a gross oversimplification but I think it helps answer the question for those people who are still asking it.

I don't think a good answer is that SR demands that it isn't possible because I think the people who are asking the question are really asking why SR demands that it isn't possible and for that, you need to not use SR but stay in one reference frame.

 

[Dale]

What if I said, by your logic, a rocket could exceed the velocity of light?

That is not correct, nor is it implied by bcrowell's correct statement.

 

[Buckleymanor]

There are many ways that velocities greater than c can appear in relativity without violating any of the above considerations. For example, one can point a laser at the moon and sweep it across, so that the spot moves at a speed greater than c,

I can't see how that would work.
Your stood on Earth with your laser.
You point it at one side of the moon and then turn it on.
It would take the time light travels to reach that side of the moon.
You then move the laser to sweep it across the moon.
Presuming you move the laser a short distance ie. the apparent size of the obseved moon from where you are stood at say 99% of the speed of light.
Why should the end of the laser the spot move faster than c across the moon.
Each part of the movement or sweep would be a different position and the light would have to traverse along that new position at c before it reached the moon.
Much the same way as water from a hosepipe or a rigid stick would bend if you tied to sweep it.
The light would allso bend in an arc and travell at a speed less than c across the face of the moon.
Maybe it is what you mean by appear to travell at a velocity greater than c but in reality it can't.