A Couple of Questions About the Speed of Light.

Factual Questions
1

Just a couple of questions about Einstein’s famous laws, involving the speed of light specifically.

As we all know (or most of us do, in any event), if matter were to go the speed of light three things would happen. Time would stop. Its length would shrink to zero. And its mass would be infinite. Propelling infinite mass would involve infinite energy. So that “should” be impossible. Just one thing about that that isn’t clear to me. If something had zero length, wouldn’t have zero mass? No length equals no mass? Am I wrong? Please make your answer as complicated as necessary to explain this question. But use simple language too (we don’t all have a doctorate in physics, you know).

Second, light, or more specifically photons, can go the speed of light. This is because they have energy, but no mass (correct me if I am wrong about this, though). But Einstein proved energy is mass, and mass is energy. So if they have ANY energy at all, then they have mass? No? Again, tell me where I am wrong about this.

(BTW, I might as well tell you. I have a theory about this. And it goes, Einstein wasn’t entirely right. His equations made sense on paper. But in reality, photons have a slight mass [that is why they can’t escape black holes]. But things that go the speed of light, in fact, do NOT have infinite mass. Again, it is just my pet theory. Things in the real world sometimes are a little different than they are on paper. As I said, just my pet theory.)

Also, if photons don’t have mass, why can’t they then go FASTER than the speed of light, sometimes? If they could, they could go back in time. And that would really be neat, in more than one way, I’m sure. We still couldn’t send matter back in time. But what about a MESSAGE? Makes the mind wonder, just thinking about it.

As I said, please make your remarks sufficiently accurate, but in plain language, so we all can understand it.

Thanks in advance, to all who reply:)

2

I think you are a little off on that point. A singularity is a dimensionless “point” of infinite mass, so the idea of compressing something into masslessness isn’t a given. Perhaps, then, accelerating a solid object to the speed of light might turn it into a black hole.

3

The change in length and “mass” is relative to an observer in a different reference frame.

4

That’s not entirely right. Time dilation and length contraction are effects from comparing difference frames of reference, however you cannot construct a frame of reference for an object travelling at c. So whilst the limits of equations might suggest various things when making comparisons of reference frames when one frame is travelling at c relative to the other, such comparisons are nonsensical because one of the reference frames doesn’t exist! Mass dilation/increase refers to relativistic mass which is an outdated concept, but as it is impossible for an object with non-zero rest mass to travel at c, so talking about objects at c having infinite mass is again nonsensical.

Single photons have zero rest mass (we are still able to define a rest mass for a photon even though it doesn’t have a rest frame as the rest mass can be calculated from the energy and momentum). They have relativistic mass, but this is just a synonym for their energy.

There are theories of massive photons, but the point would be that if photons were massive they wouldn’t travel at c as nothing with (rest) mass can.

Rest mass, energy and momentum are all related and the only way a massless particle can have energy is if it is travelling at c (ditto momentum). We could imagine a hypothetical massless particle travelling at less than c or even greater than c without violating any physical principles, but as it would have zero energy and momentum it would be more of a non-particle than a particle!

5

And the reason that photons can’t escape a black hole has nothing to do with their energy, mass, or lack thereof. The most succinct description of the reason is that there is simply no path from the inside of a black hole to the outside. It is exactly as hard to travel from inside a hole to outside as it is to travel into the past: In fact, the radial dimension of a black hole is a timelike dimension everywhere inside the horizon.

It should also be noted, incidentally, that we’re not actually certain that photons are truly massless. An object with very low mass behaves almost exactly like an object with zero mass, for purposes of any experiment anyone’s ever come up with, and in the limit as the mass approaches zero, the behavior in every experiment approaches the massless behavior. Thus, any experiment can only ever provide an upper bound on the mass of the photon, but can never actually prove that it’s zero. IIRC, the current best upper bound is that the mass of the photon is less than about a millionth of an electron volt (for comparison, neutrinos, the lightest particles known to have a mass, are probably somewhere in the vicinity of 1 eV, and electrons, the lightest particle for which the mass is known, are 511,000 eV). Even though relatively little is known about the graviton, the limits on its mass are even tighter: At most something like a billionth of an eV.

6

Well, it’s true that accelerating something with mass to the speed of light would take infinite energy – the actual equations are very clear on that. But physicists generally now think that it’s more helpful to think of the equations as saying “it takes more energy to accelerate something as it gets closer to the speed of light”, and not talk about mass changing. The math is the same either way, but it’s easier to not make bad predictions when you’re not thinking about changing mass.

That’s the thing with describing physics in words: words are imprecise, and can mean different things to different people, and you can even reframe something using words slightly differently and still be just as accurate (or not).

So this is really hard: equations can be clear, but when you put them into words, you’re always going to be less accurate. The plainer the language the less accurate.

And so if you try to do physics based on words, rather than the actual equations and math, you’re always going to be inaccurate.

7

Or, more precisely, what gets published in scientific journals is plain language. It’s just not familiar language. Familiar language is horribly un-plain.

8

To an outside observer, a massive particle traveling near the speed of light is asymptotically flat.

9

I suppose so, though that’s not the usual usage of that term.

10

As something with a speed near that of light is viewed as being shorter, I guess it is viewed as being denser (even if you compute density as rest mass per volume and not relativistic mass per volume). So if something speeds towards or away from me at a large enough velocity, do I view it as a black hole?

I’d guess the answer has to be no as the existence of a black hole seems to be something every observer (outside of the event horizon in any case) must agree about. But why not?

11

The only problem I have with this is that “how much energy it takes to accelerate something” is how we define mass. So if it takes x energy to perform y acceleration on some object, and for another object and it takes 2x energy to perform y acceleration, what’s wrong with saying that the object is twice as massive as the first? And if the objects are the same objects, just measured in different states, what’s wrong with saying that the object changed mass? Isn’t that what “mass” means?

12

If that’s what you want unspecified ‘mass’ to mean, then sure it’s fine. But physicists have mostly agreed by now that it’s less confusing in most cases to not use that definition of (unspecified) mass. Rather than adding a relativistic adjustment to mass, they put the adjustment in the formula for momentum. If you define mass ‘how much force it takes to change something’s momentum’ (rather than how much force it takes to change velocity), then the definition still works fine.

In other words with γ the Lorentz factor, rather than saying m= γ m0 and** p**(momentum) = m v (with** F** =dp/dt), modern physicists would just say p = γ m v, which still preserves** F** =dp/dt across reference frames, but makes other formulas simpler and clearer.

13

Perhaps it might be better to say that as something approaches the speed of light, its weight increases, since weight is actually a unit of force. On Earth, we frequently consider mass and weight to be the same thing since for us, it pretty much is. On the moon, or at 0.99c, it isn’t.

Thus, you could say that a spaceship weighing 1000 pounds on Earth weighs less than that when sitting on the Moon, weighs more when trying to escape Jupiter, and weights an almost unbelievable number of times more when accelerated to 0.99 of the speed of light.

Isn’t that the definition of weight?

14

No, weight is the force exerted by gravity.

15

In Newtonian physics Energy and acceleration of a free object are related by a = m[sup]-1[/sup]dE/dx, which can be re-arranged to F=ma.

In special relativity if we insist on using this apparently ‘simple’ definition for mass, we actually end up getting something pretty obtuse. I pointed out previously that to get a definition of ‘mass’ m that of a free object that is purely how difficult it is to accelerate an object (i.e. F=ma), then m becomes the 3x3 matrix:




(m[sub]0[/sub]γ[sup]3[/sup]v[sub]x[/sub][sup]2[/sup]/c[sup]2[/sup] + m[sub]0[/sub]γ    m[sub]0[/sub]γ[sup]3[/sup]v[sub]x[/sub]v[sub]y[/sub]/c[sup]2[/sup]         m[sub]0[/sub]γ[sup]3[/sup]v[sub]x[/sub]v[sub]z[/sub]/c[sup]2[/sup]     )
(m[sub]0[/sub]γ[sup]3[/sup]v[sub]y[/sub]v[sub]x[/sub]/c[sup]2[/sup]         m[sub]0[/sub]γ[sup]3[/sup]v[sub]y[/sub][sup]2[/sup]/c[sup]2[/sup] + m[sub]0[/sub]γ    m[sub]0[/sub]γ[sup]3[/sup]v[sub]y[/sub]v[sub]z[/sub]/c[sup]2[/sup]     )
(m[sub]0[/sub]γ[sup]3[/sup]v[sub]z[/sub]v[sub]x[/sub]/c[sup]2[/sup]         m[sub]0[/sub]γ[sup]3[/sup]v[sub]z[/sub]v[sub]y[/sub]/c[sup]2[/sup]         m[sub]0[/sub]γ[sup]3[/sup]v[sub]z[/sub][sup]2[/sup]/c[sup]2[/sup] + m[sub]0[/sub]γ)

Where m[sub]0[/sub] is the rest mass, c is the speed of light in a vacuum, v[sub]x[/sub], v[sub]y[/sub] and v[sub]z[/sub] are the components of the objects velocity along the x, y and z axes and γ is relativistic gamma which is equal to [1 - (v[sup]2[/sup]/c[sup]2[/sup])][sup]-0.5[/sup].

16

Does this also apply to acceleration, since they’re equivalent?

17

Given an accelerated reference frame, yes, you can say that weight is the apparent “force” in that accelerated reference frame.