# If $c$ is constant to every observer, how can be the speed of an electron moving at $0.9c$ is not constant to every observer?

How can the speed of light, c be the same to an observer who is moving in the same direction with 0.9c and to another observer who isn't moving?

If there is an observer who is following (moving in the same direction) a photon with 0.9c speed, how can that observer see the photon moving still at the same c speed? And if somebody is moving in the opposite direction with 0.9c speed, how can that observer see the same photon (that is moving in opposite direction) moving with the same constant speed c?

Extension: I understand that SR's time dilation makes to any observer c as a constant speed. But my question is: let's say there is something moving at a little bit slower speed, lets say an electron moving at 0.9c. Is this also true for the electron, so that any observer moving at any speed, any direction would see the electron moving at constant 0.9c?

If not (and that is what I am guessing) then I dont get it. Why is it true for EM waves propagating at speed c only? Anything moving even a little bit slower then c will not be seemed to any observer moving in any direction to be moving at the same fast constant speed? Why not?

• The speed of light is a constant in all frames of reference, that is simply a law of nature, but it's direction is not constrained in any way in empty space. – user108787 Oct 7 '16 at 20:00
• Using correctly capitals is important to an usable question quality. Thus, start your senteces with capitals, but don't use all-capital words. I think your question would be a commonly asked naive layman question, but an answerable and on-topic one, b+! You only have to formulate it on a polite and correct way. Maybe it would be closed as a duplicate (questions like this were asked thousands time already here), but in the dupe you could find your answer. – peterh Oct 7 '16 at 20:37

You are mixing two different things:

1. The Special Relativity, it is dealing with the time dilatation, etc.
2. The General Relativity, it is about the spacetime curvature.

The two theories could be used from eachother independently, but although GR without SR is highly uncommon.

Both theories have a very clear math. Similar naive questions are mainly about a seemingly problem about the terminology, and not about their math. The math of (1) is not really above the high school level. The math of the GR is harder.

The answers to your questions are the time dilation. The time of the moving observers slows down (in the reference frame of the "standing" observer).

To your extension: only $c$ is invariant to Lorentz-transformations (Lorentz-transformation means if you move to another frame of reference). If an electron moves with $0.9c$, its speed will depend on where do you see that.

In an 1D linear system, you can use the relativistic velocity addition formula:

$$v_1+v_2 \rightarrow \frac{v_1+v_2}{1+\frac{{v_1}{v_2}}{c^2}}$$

Also in this formula you can see, if one of the velicities is $c$, also the result will be $c$, independently from the other velocity.

EM waves move always with $c$ is coming out from the Maxwell-equations. The proof is shorter as a page and it is only a little bit over the high school level math.

As @CountTo10 (notifiable nick) mentioned in his comment, the direction of the movement can change.

Also the wavelength of the EM waves can change for Lorentz-transformations.

• I wouldn't say that GR without SR is uncommon, I would say that it is impossible. In GR you consider diff-invariance of the metric and in SR you only consider the subset of diffs that are linear transformations. – dpravos Oct 7 '16 at 20:08
• @DavidPravos Ok, but all of the theories, incl. the Newtonian mechanics, is diff-invariant. Why would it make impossible to have a Newtonian-like mechanics with a non-trivial metric? (Note: unfortunately I can't find my source about this, but I am sure I've read about this, although it was mentioned as a highly exotic theory) – peterh Oct 7 '16 at 20:16

Velocity isn't fixed, it's relative, so you have to say what the Electron is moving relative too.

If we set up an example, lets say, you are on Earth and your friend is on Mars and he has an Electron gun and he's shooting electrons at your electron detector, the electrons leave his gun at .9c but relative to you, you have to add the relative velocities of Mars relative to Earth. That's not too different than playing catch while driving, the relative velocity of the cars is added to the velocity of the balls you're playing catch with.

Light is different, you can't add or subtract velocity to light by shooting it off a moving planet because all particles without rest-mass move at the speed of light. Each photon of light has a specific energy and wavelength. What changes is the clocks of the individual who see that light. To them, the light might appear somewhat redder or somewhat bluer depending on their relative motion towards or away from the light source and their relative clock-speed.

• thank you for the answer. so you say, that em waves are only different, because they seem to be moving at the same speed to all observers. but my question was why? so you are saying the reason for that is they change, just not their speed. but their frequency(or wavelength) changes? So different observers see em waves propagate at same speed but with different wavelength? so one observer will see the same photon have one wavelength, and another observer will see the same photon have another different wavelength? – Árpád Szendrei Oct 7 '16 at 20:39
• Explaining "why" gets complicated and a bit over my pay-grade. But to your 2nd question, yes, 2 people can see the same (not the same photon), but lets say it's a colored flashlight from one source and a specific wavelength, then 2 people can see that light as different colors, provided one is moving towards or away from the light. It's no different than the sound of a car or siren changing as it passes you, moving towards you it's higher pitch, moving away it's lower. Same sound wave, but the sound changes based on motion. – userLTK Oct 7 '16 at 20:45
• I understand this wavelength part. What I don't understand is, why is em waves different then and electron? I understand that em waves, or a phonton dont have rest mass, and thus cant have a rest frame. but still, just like you say, they are moving relative to observers. electrons are moving relative to observers too. photons are moving relative to observers too. what you are saying, is that since c is constant to any observer is like saying that photons are not moving relative to anything. they are just moving un-relative(sorry maybe its not a word) to everything else. still dont get it why? – Árpád Szendrei Oct 7 '16 at 20:49
• Light is different because it's a particle with no rest mass and having no rest mass it has to travel at C. The electron has rest mass so it can't. That's due to the Higgs field. When I think about this deeply I usually run into something that stumps me, so I'm not an expert, but the quick and easy answer is rest mass. Light doesn't have any. Both Maxwells and Einstein's equations point towards a fixed, unchangeable speed of light, but explaining why gets complicated. Someone here is bound to be better at that part than me. – userLTK Oct 7 '16 at 20:59
• yes that's where I get clueless. how can something just be c just because it does not have rest mass. it's like it's not relative to anything. – Árpád Szendrei Oct 7 '16 at 21:06

When the initially stationary observer starts moving towards the light source with speed v, the frequency he measures shifts from f=c/λ to f'=(c+v)/λ. This means that either the speed of the light relative to the observer shifts from c to c'=c+v, or the motion of the observer somehow changes the wavelength of the incoming light - from λ to λ'=λc/(c+v). The latter scenario is absurd - the motion of the observer is obviously unable to change the wavelength of the incoming light.

Answer to your question: The speed of light is different to differently moving observers, in violation of Einstein's relativity.

• Another one of your anti-physics nonsense. – Bob Bee Oct 8 '16 at 1:45

## protected by Qmechanic♦Oct 13 '16 at 13:48

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