OK, I’ve read all the previous posts on this subject I could find but I didn’t see this specific question addressed. I also realize that due to my my lack of understanding, I face derision still, I press onward.
I was watching a Neil DeGrasse video (link), in it he explains that were you in a car moving 99.999999999% the speed of light (relative to the background, what ever that may be), and turn on the headlights - you see no difference.
It took me a bit but I think I understand why, relativity.
So, hypothetical: You are sitting at a station point watching cars go by. The first convertible car drives by at 30 MPH (relative to you) and right as they pass, someone inside stands up and throws a ball forward at 30 MPH. To the occupants in the car, the ball moves away from them at 30 MPH. To you, the ball is moving at 60 MPH.
The second car comes by moving at 99.999999999% the speed of light, relative to you, and right as they pass they turn on the headlights. To the occupants, light from the headlights move away from them at the speed of light. What effect do you see?
You see the light from the headlights moving at c. That’s the fundamental fact of Special Relativity – every observer sees light travel at c, regardless of their velocity relative to other observers.
This is not quite correct. At low speeds like 30 MPH, it’s very close to correct, but the correct formula for addition of velocities is not v = v_1 + v_2; it is v = \frac{v_1 + v_2}{\gamma}, where \gamma = 1+\frac{v_1 v_2}{c^2}. At velocities that are small compared to c, \gamma is very close to 1, so the non-relativistic formula is close to correct. When both velocities are 30 mph, \gamma is 1.000000000000002.
You (the outside observer) see a car moving at “99.999999999% the speed of light“ (i.e. a blur) which is going just slightly slow than the light emitted by the headlights.
You mean from the standpoint of the outside observer? Yes, the light would be just be proceeding the car. From the forward aspect (looking into the lights) they would also be highly blueshfted because of all of the additional momentum gained from being emitted from the car moving at such relativistic speed.
From the perspective of occupants of the car the light would just travel normally (i.e. faster than they can visually perceive) because their perception of the outside world is effected by relativistic contraction; that is, for them (relative to an outside observer) time is slowed down.
It is not an easy experiment to perform: you can’t see the light crawl away from the car, as the lights and the car travel in one direction and you stand beside the track. If you move with the car, parallel to the track, at the same speed as the car, you will see the same as from inside the car: the light advancing at the speed of light. Only you don’t see light travelling away from you, you see it bouncing off objects and being reflected towards you. If you stand still the measurement is really difficult, both the car and the beam of light are over before you are aware of it. If you set up detectors along the path you somehow know both the car and the light will be travelling along the signal from the detectors to you will only travel at the speed of light or less. You will be able to infer with hindsight that the light was travelling a bit faster than the car, heavily blueshifted and all what Stranger_On_A_Train wrote, but it is not like you could see it. You can only calculate it and believe it. It may sound like nitpicking, but the details of the experimental setup are relevant in such a case, I believe.
From a practical standpoint, yes. Most experiments testing predicted effects of special relativity require either a lot of inference or involve measurements of celestial phenomena (i.e. the anomalous precession of Mercury) because such phenomena are not observable in everyday activity in the way Galilean relativity (e.g. the example of the pitcher throwing a ball from a moving car) is.
Quantum mechanics is even more challenging because although many thought experiments implicitly assume a ‘classical’ (non-quantum) observer, all actual systems are fundamentally quantum in nature and there is no way to observe a quantum system without interacting with it. Understanding this is key to accepting that the double slit experiment is not a paradox but just a consequence of measurement.
But what do you think you are filming? The camera you linked to is working with laser beams that stroboscope the observed object, the stroboscope acting like a shutter because except for the laser everything is dark. You are in a closed, sealed room. That will not be the case with your car, and you can not use stroboscopes as a shutter to film a beam of light, particularly not if the light beam does not point in your direction.
And if the car and the light beam point in your direction you will be run over with fascinating relativistic effects involved in a very short time. This is a different problem, particularly for you.
I insist: you can not see light that is not either pointing at your retina or reflected form other objects in the direction of your retina. Light is invisible if it does not travel towards you. I am not disallowing nothing, just pointing at the conceptual difficulties of your experiment.
The car is driving next to a wall. The light illuminates the wall. But I still say for a thought experiment, it’s valid. In this thought experiment, no one complains that you wouldn’t be able to observe the trajectory of the light ray.
It is easy to see the beam of light in the thought experiment you just linked to, just blow some smoke. You will not see the individual photons, but you will see the path all photons take. You are not moving with relativistic speed in the elevator, I don’t see the problem.
I think the situation is different in the OP. But OK, assume you could make the car drive through a mist, tenuous enough as not to destroy the car, but dense enough to see the scattered light. Then you would see what Stranger_On_A_Train wrote.
And BTW: if the car has a rest mass of 1 ton, at the speed you postulated it would have a mass of over 12,000 tons. If my calculations are correct and I did not mess up with the many zeroes.
Another weird thing is that when the car is passing directly beside you, it will appear rotated because of Terrell Rotation, so you would only see the tail lights, not the head lights. This is because of the aberration of light.
The experiment in question is routinely carried out implicitly in particle accelerators. Perhaps the most analogous version would be at a synchrotron light source, wherein electrons traveling near the speed of light are tickled by magnetic fields to induce the emission of (usually) X-rays. The X-rays could be said to “crawl” away from the high-speed electrons. Their relative speeds are measurable as the X-rays and electrons continue through bits of instrumentation. The difference in speed between the X-rays (light beam) and electrons (metaphorical “car”) is on human scales, like a meter per second or so, depending on the specific machine’s specs.
Such light sources are just an example. Two things moving at or near the speed of light with measurably different speeds or travel times across an apparatus is quite routine, including in cases where one item was in some sense “emitted” by the other.
(Edited for additional detail: Note that the speed difference in the above “light source” X-ray vs. electron case is very small and not practically distinguishable from zero because the electrons are moving very very close to c, but that’s the point – the electrons don’t lag behind the X-rays but rather stay seemingly neck-and-neck with the X-rays. In other applications, though, the speed difference can be larger and more experimentally salient, but the point remains that any emitted light will be seen as travelling at c by an observer who also sees the emitting object moving at close to c.)
You don’t need super-high speeds to measure relativistic effects. I’ve done experiments with middle-schoolers where we measured relativistic effects from objects moving at 1 cm/s.
Each kid had a foot of copper wire, a C-cell battery, and a nail. Hook up a foot of copper wire to 1.5 volts, and the electrons in the wire will be moving at 1 cm/s. Wrap the wire around a nail, and it’ll make an electromagnet, capable of picking up small things like paperclips. That magnetism is a direct result of relativistic effects on the electrons due to their 1 cm/s motion.
While that is true that this ‘megnetostatic’ effect of charges through a coil is a result of special relativity (and in fact, if you study Maxwell’s complete set of equations instead of the four reduced Maxwell-Heaviside equations that are presented in undergraduate courses, special relativity is an inevitable consequence), it isn’t intuitively obvious that this is so from performing or viewing this experiment; it has to be inferred from an understanding of the relationship between charge density and the speed at which those charged particles can move in a particular medium (in this case, the copper wire). Feynman’s Lectures, Vol 2 describes this (section 13-6 and -7) but while it is all algebra I think the concepts are advanced for even a talented high school physics student.
Fundamentally, special relativity cannot be intuited from everyday experience; it has to come from building a mental model of behavior that is very different and based upon applying the Lorentz contraction to the cartesian-like topography that we normally use to measure and interpret motion of objects. It isn’t terribly difficult once you grasp that all motion is relative to the invariant speed of light (and indeed, everything is moving through spacetime at c, with objects at rest relative to a particular frame are moving only along the time axis at that speed in that reference frame) but it is totally at odds with how we learn to interpret the world through normal interactions.
