# Making observations from a particle at 0.99c, will all “slow” objects move at 0.99c?

I'm imagining an observation from a particle at near light speed. Then, I believe I should be able to say that this particle is standing still relative to other moving objects.

If this is true, would a slow object (like the earth) seem to be moving at close to light speed relative to this particle?

If the answer is yes, then my problem is that it should not be possible to have the earth moving at such tremendous speed. AFAIK, nothing but mass less objects can move at light speed, so wouldn't it be strange if some large object can almost obtain this speed (0.9999999999c) just by changing observation position?

The answer is yes: one "everyday intuition" that still holds in special relativity is that if velocity of observer B relative to A is $v$, then the velocity of A relative to B is $-v$, just as in Galilean relativity. This symmetry is known as relativistic reciprocity.

As to your concerns about the Earth "moving at tremendous speed": imagine an electron at the center of the Earth, and imagine you're somewhere outside the Solar System and then accelerate to $0.99c$. You would see the electron moving at $0.99\,c$. If you have no problem with the electron's relative motion (and they are routinely accelerated to much nearer to the speed of light than this in particle accelerators), then you should have no problem with the Earth's motion: otherwise your change of motion alone would impose relative motion between far off objects that were formerly rest relative to one another.

Further Question from OP

... but I thought it was impossible for large objects to have these kinds of speed? You can continue this kind of reasoning (ever more closely to c), until the earth in-fact maintains almost the speed of light - shouldn't that be a problem? As far as I know, only objects without mass could do that. Is there really no time-dilation (as seen from the electron) that prevents this kind of reasoning?

Ah, I think I see what you're getting at. You're right that only massless objects can have a velocity of $c$. But any massive object can have any relative velocity of finite rapidity (i.e. $<c$, even if less by only by an epsilon's whisker) relative to anything else. The time / length dilation factors are simply geometric properties: pretty much analogous to the trigonometric functions that enter the transformation matrices for rotations (a They can have any finite value. The other limitation is that kinetic energy must be supplied to a massive object to change its motion state, and that kinetic energy is given by $(\gamma - 1) \,m_0$, where $\gamma = 1/\sqrt{1-(v/c)^2}$ as measured from its inertial frame before the motion state change (witness that energy, too, is relative and depends on the reference frame it is measured from). Thus this needed energy supply diverges as the relative speed change approaches $c$. But as long as you can supply the energy to it, there is no problem, at least in theory.

But there certainly would be practical relativistic problems in accelerating to very high speeds relative to massive stuff around you; see Randal Munroe's "What If" article "Relativistic Baseball" where he studies some of these problems for a massive object boosted to, co-incidently, $0.9\,c$ relative to the atmosphere around it.

• Thanks for the answer - but I thought it was impossible for large objects to have these kinds of speed? You can continue this kind of reasoning (ever more closely to c), until the earth in-fact maintains almost the speed of light - shouldn't that be a problem? As far as I know, only objects without mass could do that. Is there really no time-dilation (as seen from the electron) that prevents this kind of reasoning? – mortensi Jan 4 '17 at 6:54
• @mortensi See my changes. – WetSavannaAnimal Jan 4 '17 at 10:24
• Thanks again, very helpful. It seems like there is a consensus on your answer - so I guess you're quite right. It's still very troubling, since now the earth it self can be said to have (almost) light speed, with all the relativistic effects (time-dilation?) compared to the photons out there.Even dodging the acceleration issues, it still seems very strange. Wouldn't it imply that the time for a photon proceeds "normally", while the earths time is moving slowly? While it's the opposite measured from earth. How can both views be correct... Maybe this will be a new question:) – mortensi Jan 4 '17 at 13:02