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To start: Not a physicist, just a curious idiot. Forgive my lack of understanding if there is something fundamental I miss here.

I've seen similar questions to mine, and answers relate specifically to mathematical processes at a geometric level which is beyond me, and (also beyond me) quantum theory - rather than simple to understand physical processes - especially in relation to a higgs mechanism presuming an increasing object mass as velocity increases. The answers are confusing and not consistent with any of my understandings of physical reality (I repeat: a curious idiot :)).

The problem I have: Relativistic mass increases because speed does? The presumption this is connected to momentum and kinetic potential energy (it is potential as it doesn't ACT on anything) is really dissonant to me. There seems to be no functional mechanism for Kinetic Potential Energy to create Mass which would constrain acceleration profiles of an object in a vacuum.

Is it instead that the "mass increase" mentioned at speed approaching $c$ is consistent with the increase of photonic pressure around an object acting as a barrier to further acceleration?

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Actually, this kind of questions really depend upon what would you accept as an answer.

But we can just avoid the concept of mass increasing with velocity and just talk about less confusing stuff.

For example, the energy of a massive object, rest mass $m_0$ never changes, goes with velocity $\vec v$ as $$\tag1E=\frac{m_0c^2}{\sqrt{1-\frac{\vec v\,^2}{c^2}}}$$ which clearly goes to infinity when you making it go faster and faster, approaching the speed of light. This means that you can never give it enough energy to ever reach the speed of light.

Is this sufficient for you to accept that it is impossible for massive objects to reach the speed of light?

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  • $\begingroup$ Thanks naturally inconsistent! Would I be correct in describing relativistic mass, not as Mass, but rather the energy burden required to move the object when approaching C? Or does relativistic mass display all relationships that rest mass does? Just trying to get a better understanding of this. Right now, I'm confusing myself thinking there must be an equal an opposite reaction creating the relativistic mass. Part of the reason for this is that photons describe same constraints in energy at infinity. From 1-10 is that dumb? Just trying to wrap this small brain around it. $\endgroup$
    – Sam Hale
    Jun 20 at 5:46
  • $\begingroup$ As a general rule, it is just a bad idea to teach by the concept of relativistic mass. Just talk about energy, which is easy to understand: Everybody agrees that you need to provide kinetic energy to a body for it to move faster, and here it is clear that you need infinite amounts of it just to reach the cosmic speed limit. The only mass I talk about is the rest mass, and that does not change for any fundamental object. The nice thing about talking with only these things is that it is much less confusing. $\endgroup$
    – naturallyInconsistent
    Jun 20 at 6:24
  • $\begingroup$ Thanks for clarifying! $\endgroup$
    – Sam Hale
    Jun 20 at 6:29
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As velocity goes up, the relationship between energy and momentum changes, in a manner exactly as if the mass of the object were increasing. But these days, all the discussion around this topic is cast in a form where the rest mass of an object is an invariant quantity. The experts here can explain why this is more useful than the earlier paradigm, which was that the thing gets heavier ("relativistic mass") as it speeds up.

(As an aside, if you read the white paper on the history, design, construction and operation of the Stanford Linear Accelerator (dating back to the mid-1960s), you see explicit references to "relativistic mass" throughout- and yet they still got the right answers to all their questions.)

There is no "photon pressure" that restricts velocities to less than c.

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  • $\begingroup$ Thanks Niels. I'll go have a look and see what I can make out. Makes me even more curious though, what effect radiation pressure would have at relativistic speeds. I would assume at that point intensity of incident light would be incredibly high. $\endgroup$
    – Sam Hale
    Jun 20 at 4:03
  • $\begingroup$ this is a complicated business, which is why I leave it to the experts! -NN $\endgroup$
    – niels nielsen
    Jun 20 at 4:26
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    $\begingroup$ @SamHale The point is that even if there is no radiation to exert any pressure at all, an object with mass still cannot reach the speed of light. $\endgroup$
    – Ghoster
    Jun 20 at 4:59
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The finite speed of light is a consequence of relativity. It can be derived algebraically in a completely model independent manner from the fact that the universe is (locally) a three dimensional geometric space that's isotropic and homogeneous, that all physics is relative and that there is a meaningful notion of time (which assumes that physical systems have a property called "energy", which can spread out spatially) from which we can formulate the well known definition of "velocity". Nothing even as remotely complicated as "light pressure" is needed.

If we drill down into this a little bit, then there still remain some fundamental questions, like why the universe happens to be three dimensional and why it has a locally conserved quantity like energy (which is equivalent to saying that time measurement is possible with systems called "clocks") to begin with. This we can't solve at the moment as far as I know. However, the remainder of special relativity is a series of basically unavoidable logical consequences (at least I am not aware of any loopholes) once we accept these fairly general observations about the structure of spacetime.

Wikipedia has an article about this derivation that contains the crucial steps: https://en.wikipedia.org/wiki/Derivations_of_the_Lorentz_transformations

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  • $\begingroup$ Awesome! Thanks FlatterMann! Going to rabbit-hole the hell out off this. Hope you don't mind me returning when I have questions! Really appreciate the guidance on where to look! $\endgroup$
    – Sam Hale
    Jun 20 at 5:54
  • $\begingroup$ Finite speed of light comes from Maxwell's. $\endgroup$
    – naturallyInconsistent
    Jun 20 at 6:25
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    $\begingroup$ Finite speed of light comes from Maxwell's. Historically, yes. But there would still be an invariant speed even if electromagnetism and light didn’t exist. $\endgroup$
    – Ghoster
    Jun 20 at 7:57
  • $\begingroup$ @naturallyInconsistent Gravity: hold my beer. No offense, but what comes first are geometry and symmetries. After that everything is derived. The big miracle is what makes geometry, at least in my mind. I have found absolutely no answers to that in the literature that I have seen, so far. $\endgroup$
    – FlatterMann
    Jun 20 at 16:05
  • $\begingroup$ So, this is the follow up: Does relativistic mass only apply to the external surface of the object bundle, or would internal objects - travelling at relativistic speeds within an object - be capable of moving around within it? From the discussion of relativistic mass (energy required to move) and Lorentz transformations, I THINK the interior of the object at fractional C would adhere to the same principles as the exterior (significantly more energy to move about within a structure)? Reason I ask is that the fastest objects detected (Blazars) still display plasmic interactions. $\endgroup$
    – Sam Hale
    Jul 2 at 9:47

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