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If we exert force on an object which would be travelling at near light speed, to an extent to make it move greater than speed of light in vacuum, what would happen? If object doesn't move faster than light, what happens to that excess force?

Is this experiment been done? What would happen if we exert force on light travelling at its maximum speed?

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  • $\begingroup$ "to an extent to make it move greater than velocity of light" - I've voted to close your question for the reason that non-mainstream physics is considered off-topic here. $\endgroup$ Nov 4, 2018 at 2:40
  • $\begingroup$ @AlfredCentauri is referring to the fact that there is no amount of force that can accelerate an object from below light speed to above light speed. (According to Newtonian mechanics, you can of course accelerate objects past light speed, but according to relativity --- which appears to be the context of your question --- you can't.) $\endgroup$
    – WillO
    Nov 4, 2018 at 2:57
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    $\begingroup$ @AlfredCentauri Note that the OP says "which would" not "which will", and then he or she goes on to suggest that the object might not. I think it's a mainstream physics question. You might have misinterpreted the intention of the question. $\endgroup$
    – garyp
    Nov 4, 2018 at 3:02
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    $\begingroup$ Please do not make your post look like a revision table, instead just seamlessly integrate the new material into the post. There is an edit history button at the bottom of the post for those interested in seeing what changed. $\endgroup$
    – Kyle Kanos
    Nov 5, 2018 at 11:10
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    $\begingroup$ This is a perfectly reasonable question, and I'm baffled by the close votes. The OP just wants to understand the answer to a FAQ about special relativity. That doesn't mean it's not a question about mainstream physics. $\endgroup$
    – user4552
    Nov 5, 2018 at 16:17

2 Answers 2

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If you apply a force (in the direction of motion) to an object with mass, moving close to the speed of light, the object will accelerate and its speed will become even closer to the speed of light. But no amount of force can make it reach, or exceed, the speed of light.

The reason that objects behave this way is that momentum is not $m\mathbf{v}$ as Newton thought; it is in fact $m\mathbf{v}/\sqrt{1-v^2/c^2}$ as Einstein realized. Applying a constant force will cause the momentum to increase indefinitely, but the momentum becomes arbitrarily large as the speed approaches $c$.

There is no way to exert force on light. It always travels (in vacuum) at the speed of light, and cannot be sped up or slowed down.

Why? Well, photons don’t have charge, so they don’t feel electromagnetic force; in fact they carry electromagnetic force. Nor do they feel the strong or weak nuclear forces. They do feel gravitational force, but it doesn’t make them move faster or slower. (In General Relativity, they just move on lightlike geodesics.) These four forces are all the fundamental forces, as far as we know.

There is plenty of experimental evidence for these facts.

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    $\begingroup$ Thank you for the answer. Why is there no way to exert force on light? $\endgroup$
    – Sensebe
    Nov 4, 2018 at 2:57
  • $\begingroup$ From theory, it may be saying the impossibility, but practically what would stop us from exerting force on light? $\endgroup$
    – Sensebe
    Nov 4, 2018 at 3:10
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    $\begingroup$ Photons don’t have charge, so they don’t feel electromagnetic force; in fact they carry electromagnetic force. Nor do they feel the strong or weak nuclear forces. They do feel gravitational force, but it doesn’t make them move faster or slower. (In General Relativity, they just move on lightlike geodesics.) These four forces are all the fundamental forces, as far as we know. $\endgroup$
    – G. Smith
    Nov 4, 2018 at 3:10
  • $\begingroup$ Related: Why doesn't gravity speed up light? $\endgroup$
    – Sensebe
    Nov 4, 2018 at 3:13
  • $\begingroup$ Your previous comment seems to belong to answer for the completion of the answer. $\endgroup$
    – Sensebe
    Nov 4, 2018 at 3:37
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Its speed would get yet closer to that of light, albeit tending to infinitesimally so as the initial speed tends towards the speed of light; and the mass would increase without bound. It becomes simpler to think of it in terms of putting energy into the particle, rather than applying force to it. You could well say that as the body's motion exchanges the Newtonian regime (speed a small fraction of c) for the ultrarelativistic regime (rest mass energy m₀c² a small fraction of kinetic energy), increase in speed for a given small increase in momentum (small fraction of m₀c) is exchanged for increase in mass for a given increase in energy (that doesn't have to be small relative to m₀c²). This phenomenon is routinely observed: for physicists working with particle accelerators, it's as routine a phenomenon as vehicles passing along the road is to a city dweller; and also it's why an elementary cyclotron has an upper bound on the energy to which it can accelerate protons of ~42MeV.

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    $\begingroup$ Modern treatments of special relativity generally avoid using relativistic mass. It can lead to incorrect results if you aren't very careful. See physics.stackexchange.com/questions/133376/… and the linked questions for details. $\endgroup$
    – PM 2Ring
    Nov 5, 2018 at 13:06
  • $\begingroup$ Do they! That's interesting. I'm abitt oldschool ... about prettymuch everything! I'd be interested to see how it's reframed. One cute little recipe that I'm fond of is the one that has ... can't remember what they call it now ... haste, or something - atanh(β). $\endgroup$ Nov 5, 2018 at 13:11
  • $\begingroup$ You're thinking of rapidity, which is a convenient measure of speed in relativity because it does add linearly. $\endgroup$
    – PM 2Ring
    Nov 5, 2018 at 13:16
  • $\begingroup$ That's it yes! - rapidity. I do like that formulation & the linear adding of it. I'm going to campaign now to have it renamed "haste". You joining me!? $\endgroup$ Nov 5, 2018 at 13:23
  • $\begingroup$ @AmbretteOrrisey Even Einstein disliked the idea of ”relativistic mass”. See the Wikipedia article “Mass in special relativity”. The preferred “reframing” is in terms of energy, momentum, and (invariant) mass. Energy is the temporal component of a Lorentz 4-vector. Momentum is the spatial component of that same 4-vector. Mass is the invariant “length” of that 4-vector, left unchanged by Lorentz transformations. $\endgroup$
    – G. Smith
    Nov 5, 2018 at 16:59

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