# Is it possible to see objects move faster than c?

## Main Question or Discussion Point

Just want to start by saying some of the understanding that a lot of the major contributors show on this forum is amazing! (bows very low) Then the ability to convey that to others is fantastic!

As the title suggests, is it possible to observe something 'apparently' travel faster than the speed of light?

Hypothetically:
Everything is stationary in space.
The moon is at a distance of 2 light seconds from earth. A rocket is launched and attains c instantaneously, then takes the two seconds to travel to the moon.
There are 4 observers, one observer on the surface of the earth, one observer on the landing site on the moon, one observer at the midway point close to the trajectory path, and the last at the midway point but 1 light second to the side of the trajectory path. They all have watches which are synchronized and the launch time of the rocket is at 12:00.00pm (earth time).

The observer on the earth 'sees' the rocket leave @ 12:00.00 and take 2 seconds to get to the mid point, and 4 seconds to get to the moon @ 12:00.04

The observer on the moon 'sees' the rocket stationary on the surface of the earth till 12:00.02, then magically appear next to him @12:00.02

The observer at the mid point sees the rocket stationary till 12:00.01, then passes him at the same time, and goes on seem to take another 2 seconds to get to the moon @ 12:00:03

But the interesting observation would be from the point 1 light second to the side, they would 'see' the rocket leave the launch site @ 12:00.014, get to the mid point @ 12:00.02, then land on the moon @ 12:00.034.
The first half (1 light second) of the journey would appear to take .6 of a second, then the remaining half (1 light second) would take 1.4secs. The whole journey would appear as it took the actual 2 seconds, but the first half and second half at differing speeds.

So, is that observation possible or am I missing something?
I assume that the apparent colours of the rocket would be shifted for the observers during the trip also.

Damo

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mfb
Mentor
A rocket is launched and attains c instantaneously
You probably mean "something close to c, but not c".

That observation is possible, but it is not what "observed velocity" usually means. The observer 1 light second to the side could measure the distance of the rocket at those 3 points, and calculate the light delay for him. After subtracting those times from the observation, he will see a uniform motion with something close to c. And all other observers at rest relative to him & earth & moon will agree.

I assume that the apparent colours of the rocket would be shifted for the observers during the trip also.
Right. Together with the length of the rocket.

Borek
Mentor
You probably mean "something close to c, but not c".

That observation is possible, but it is not what "observed velocity" usually means. The observer 1 light second to the side could measure the distance of the rocket at those 3 points, and calculate the light delay for him. After subtracting those times from the observation, he will see a uniform motion with something close to c. And all other observers at rest relative to him & earth & moon will agree.

Right. Together with the length of the rocket.
Yep, you are correct, it wouldn't travel at the speed of light, but for the hypothetical question I didn't see that being a problem.

I didn't actually use the term "observed velocity", but looked it up to find a definition. How would the "observed velocity" at the 4th observation point 'look' different to what I described? He would 'see' the rocket leave the earth at √2 seconds after 12:00, 'see' the rocket at midpoint at 12:00.02, then 'see' the rocket land at 12:00.02(+√2sec). So the "observed velocity" would be greater than c for the trip to the mid point, and less than c from midpoint to the moon. Correct?
All of the observers would be well aware that their own reference frame would give the results they are seeing. 4th observer at off centre midpoint would know that the rocket doesn't change velocity during transit, but its 'apparent' velocity (to him) does.

Thanks Borek, that link shows exactly what I was thinking may happen (but in far more detail).

Thanks guys.

Damo

russ_watters
Mentor
....because it isn't an object, so it isn't relevant to the OP's question.

I like to answer this question with another question: can you hear an object moving faster than the speed of sound? The OP had it right, though, so there isn't much left to discuss. One thing I'll point out though is that you are describing observers relative to the light cone the rocket. It is very similar to the mach cone of a supersonic aircraft. Essentially -- if you're in the mach cone, you can hear the airplane. Outside it, you can't. The observer on the moon is not inside the light cone of the launched rocket, so doesn't see it coming.

Also note, you don't need to be moving at the speed of light/sound for this to be an issue. In the OP's example, the observers on Earth and on the moon see two different sets of events because of their positions. Since the rocket is "chasing" the light, the observer on the moon always sees the trip being shorter than the Earth based observer, no matter how fast/slow the rocket is traveling. This is also why it is easier to hear something moving away from you than toward you.

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[..] Thanks Borek, that link shows exactly what I was thinking may happen (but in far more detail).
I find your example much clearer than the presentation in Wikipedia!

Just look up at the night sky. The stars you see are apparently whizzing around the earth at many millions of times the speed of light.

russ_watters
Mentor
Uh, no they're not!

Somewhere on my readings here in the forums i happen to read about galaxy can move faster. it involves the apparent expansion of space.. i lost that thread sorry

mfb
Mentor
The distance between us and another galaxy can increase faster than c due to the expansion of space between us. This does not mean that the galaxy moves faster than c.

oh i see.. distance is not an object too

oh i see.. distance is not an object too
Space itself is expanding. This causes all galaxies to move away from eachother without requiring velocity. Hence, the speed of light does not apply.

russ_watters
Mentor
Yes, and "those galaxies" are not "the stars we see". All of the individual stars we see are in our galaxy.

At any point in time ,our (galaxy) have relative speed to any galaxy..different frames of reference w/ same physics.. but as the space expand w/ accelaration can the relative speed exceeds 1?

or we are we co-moving with them even the distance between us galaxies increases

refer #12

mfb
Mentor
All of the individual stars we see are in our galaxy.
Well, not always.
In addition, supernovae can outshine their entire galaxy, so it is possible to study them as individual stars as well. Individual novae can be visible, too.

A.T.
Just look up at the night sky. The stars you see are apparently whizzing around the earth at many millions of times the speed of light.
In the rotating frame of the Earth they are moving FTL. The c limit applies only to inertial frames.

HallsofIvy
Homework Helper
Yep, you are correct, it wouldn't travel at the speed of light, but for the hypothetical question I didn't see that being a problem.
Even in a "hypothetical question" about relativity, you cannot assume things that violate relativity. That would be like asking 'assuming relativity is NOT true, what would relativity say about this'!

Even in a "hypothetical question" about relativity, you cannot assume things that violate relativity. That would be like asking 'assuming relativity is NOT true, what would relativity say about this'!
To make the question easy to read, understand, make visually appealing and prevent lots of minute adjustments to the nth degree for no gain, I used the speed of light for the speed of the rocket. There are sooooooo many flaws and contradictions to nearly every conceivable force, law and amount in that one little thought experiment, that concentrating on making 'it' fit relativity would be pointless, as the next bloke who wanted to pull the question to bits would say it would never happen because there wouldn't be enough energy on the planet to accelerate something of that mass that quick, or that there is no such material in existence in our universe which could be accelerated like that, or that the guy at the mid point or even landing destination would be wiped out by the rocket before they had a chance to update their data on facebook. Thus, the senario is hypothetical, it doesn't make the results any different picturing the rocket rather than a photon.
The rocket idea seemed far more plausible than suggesting that I whipped out God's torch, turned it on and it shot out a photon the size of a rocket so that someone 450,000km could see it clearly from the motionless platform positioned in the middle of nowhere which just happened to be in the exact vantage point needed.

Damo