Shooting a gun at light speed?

[OneOnOne1162]

Hypothetically, if you were on a ship that was travelling at just below c (for example 299792457,9 m/s) and you fired a gun at another person on that ship from where you were sitting in the direction that the ship was moving, what would happen?

Edited April 7, 2016 by OneOnOne1162

[swansont]

Hypothetically, if you were on a ship that was travelling at just below c (for example 299792457,9 m/s) and you fired a gun at another person on that ship from where you were sitting in the direction that the ship was moving, what would happen?

In your frame it would move at some speed u. To an observer seeing your ship moving at v, it will move at (v+u)/(1+vu/c^2)

 

Nobody will see it as moving at or above c

[Thorham]

Nobody will see it as moving at or above c

Exactly. The bullet won't ever reach the speed of light. You could be traveling at 99.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 percent of the speed of light, and it would make no difference at all.

[OneOnOne1162]

Exactly. The bullet won't ever reach the speed of light. You could be traveling at 99.9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999 percent of the speed of light, and it would make no difference at all.

 

 

In your frame it would move at some speed u. To an observer seeing your ship moving at v, it will move at (v+u)/(1+vu/c^2)

 

Nobody will see it as moving at or above c

 

Okay, I figured something like that would happen. The universe is weird.

[Mordred]

Conceptually relativity can often boggle the mind. Greater study will often remedy the weirdness behind it.

[OneOnOne1162]

Conceptually relativity can often boggle the mind. Greater study will often remedy the weirdness behind it.

 

Well, if what I've read in the past is correct the reason why things cannot go faster than light is because mass and energy are equivalent and at some point if you keep adding energy to go faster you hit a maximum point (since you continuously need more energy to accelerate). And of course, there's the time dilation effects where when you travel at a greater speed the flow of time changes for you.

 

But the reason why I found this weird is I'm not sure how, if the first thing is true, the bullet can move at all. The conventional stuff I've heard about relativity (you know, the change in time experienced depending on speed and such) would lead me to the conclusion that the previous commenters said, but the very first thing made me wonder about that. I'm assuming it has to do with the fact that the energy that IS added to the bullet speeds it up a tiny bit in comparison with the rest and that because time is dilated it seems to be going normal speed? I don't know. I'm not entirely sure if I understand that part.

Edited April 7, 2016 by OneOnOne1162

[Externet]

Now replace the gun and bullet with two flashlamps. One aimed forward, the other backwards...

[OneOnOne1162]

Now replace the gun and bullet with two flashlamps. One aimed forward, the other backwards...

 

Well, I've already that particular example in the past. But light doesn't have mass, a bullet does.

[Mordred]

A good way to start learning this is to study relativity velocity addition.

 

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html

Hyperphysics has a decent enough calculator to play around with.

 

One aspect to be careful on is speed as measured by which observer.

 

That's covered under the site posted.

Edited April 7, 2016 by Mordred

[Delta1212]

 

Well, if what I've read in the past is correct the reason why things cannot go faster than light is because mass and energy are equivalent and at some point if you keep adding energy to go faster you hit a maximum point (since you continuously need more energy to accelerate). And of course, there's the time dilation effects where when you travel at a greater speed the flow of time changes for you.

 

But the reason why I found this weird is I'm not sure how, if the first thing is true, the bullet can move at all. The conventional stuff I've heard about relativity (you know, the change in time experienced depending on speed and such) would lead me to the conclusion that the previous commenters said, but the very first thing made me wonder about that. I'm assuming it has to do with the fact that the energy that IS added to the bullet speeds it up a tiny bit in comparison with the rest and that because time is dilated it seems to be going normal speed? I don't know. I'm not entirely sure if I understand that part.

 

What you said at the end is essentially correct, although there is no "maximum point" so much as a limit that you can continuously approach but never reach.

 

You know the CoverFlow effect that's used sometimes for slideshows, and especially for music libraries, where the whatever the current image you are viewing is displaying normally front and center, and then off to either side the images is a visible series of other images that you can scroll through, and as you get further from the current image in either direction, the images get more and more scrunched together? So a bit like this:

 

 

That's how I conceptualize frames of reference, where each image is one frame, and there are an infinite number of images extending out in either direction, but since they get more and more scrunched together, they never quite reach the edges of the frame. The central image is your rest frame. The "further" an image is from your frame of reference (i.e. the larger the velocity relative to your own rest frame), the more scrunched it appears to be, and the closer it seems to be to the images adjacent to it. If you scroll over and make that image your rest frame, however, the image on either side will appear more spread out, as it looks in the center of the above image.

 

A change in frames is really a change in velocity. So to get from one image to the next, you would need to accelerate until you reached whatever speed that image represents. Now, if you were to look at someone who is currently in a frame way at one end of this image (i.e. moving with a high velocity relative to you), they would appear length contracted and time dilated, and if they were to accelerate, they would continue moving further and further along the images. But each change from one image to the next would constitute a smaller and smaller "distance" along the line as each image (from your perspective) gets more and more scrunched together. And, of course, moving along the images in the line, they can never leave the slideshow because the images don't extend beyond the edge of the screen. They just continually get closer and closer to it extending on to infinity.

 

For a practical example of how this relates to the question, we'll say that a gun accelerates a bullet to the point that it is five "frames" away from the shooter (remembering that a frame = a relative velocity), If you are firing from the center image, the bullet appears to be going a certain amount faster than the gun in the rest frame. If someone in one of the frames at the edge fires the gun, the bullet will move the same five frames, but since the frames at the edges, from your view, look like they are closer together, the relative difference doesn't look as great as it would if you were viewing it from the frame of the gun.

 

 

That's a little more muddled than I might have liked, and I probably need to work on explaining the metaphor a bit more simply. I know it isn't the easiest one in the world to grasp because it requires thinking of velocities as a locations along a line with distance representing relative speed (and in a more strictly accurate analogy, the "line" would extend in every direction instead of just left and right), but this is the one that I use in my own mind and that makes it easiest to hold a lot of the concepts in my mind. Hopefully it will be of some help.

 

 

Edit: Heh, now I just had an idea for a little interactive tool that uses the coverflow set up, but with a series of continuously running animations that you can accelerate between by scrolling and that display proper time dilation and length contraction depending on your relative distance from them along the "velocity line." If I stuck clocks on them, you should even be able to pull off your own twin paradox experiment.

 

Hm...

Edited April 7, 2016 by Delta1212

[OneOnOne1162]

 

What you said at the end is essentially correct, although there is no "maximum point" so much as a limit that you can continuously approach but never reach.

 

You know the CoverFlow effect that's used sometimes for slideshows, and especially for music libraries, where the whatever the current image you are viewing is displaying normally front and center, and then off to either side the images is a visible series of other images that you can scroll through, and as you get further from the current image in either direction, the images get more and more scrunched together? So a bit like this:

 

 

That's how I conceptualize frames of reference, where each image is one frame, and there are an infinite number of images extending out in either direction, but since they get more and more scrunched together, they never quite reach the edges of the frame. The central image is your rest frame. The "further" an image is from your frame of reference (i.e. the larger the velocity relative to your own rest frame), the more scrunched it appears to be, and the closer it seems to be to the images adjacent to it. If you scroll over and make that image your rest frame, however, the image on either side will appear more spread out, as it looks in the center of the above image.

 

A change in frames is really a change in velocity. So to get from one image to the next, you would need to accelerate until you reached whatever speed that image represents. Now, if you were to look at someone who is currently in a frame way at one end of this image (i.e. moving with a high velocity relative to you), they would appear length contracted and time dilated, and if they were to accelerate, they would continue moving further and further along the images. But each change from one image to the next would constitute a smaller and smaller "distance" along the line as each image (from your perspective) gets more and more scrunched together. And, of course, moving along the images in the line, they can never leave the slideshow because the images don't extend beyond the edge of the screen. They just continually get closer and closer to it extending on to infinity.

 

For a practical example of how this relates to the question, we'll say that a gun accelerates a bullet to the point that it is five "frames" away from the shooter (remembering that a frame = a relative velocity), If you are firing from the center image, the bullet appears to be going a certain amount faster than the gun in the rest frame. If someone in one of the frames at the edge fires the gun, the bullet will move the same five frames, but since the frames at the edges, from your view, look like they are closer together, the relative difference doesn't look as great as it would if you were viewing it from the frame of the gun.

 

 

That's a little more muddled than I might have liked, and I probably need to work on explaining the metaphor a bit more simply. I know it isn't the easiest one in the world to grasp because it requires thinking of velocities as a locations along a line with distance representing relative speed (and in a more strictly accurate analogy, the "line" would extend in every direction instead of just left and right), but this is the one that I use in my own mind and that makes it easiest to hold a lot of the concepts in my mind. Hopefully it will be of some help.

 

 

Edit: Heh, now I just had an idea for a little interactive tool that uses the coverflow set up, but with a series of continuously running animations that you can accelerate between by scrolling and that display proper time dilation and length contraction depending on your relative distance from them along the "velocity line." If I stuck clocks on them, you should even be able to pull off your own twin paradox experiment.

 

Hm...

 

This is actually the first time I've ever heard of CoverFlow. >.<

 

But what I appear to kind of get from this is that the amount of acceleration the bullet gets compared to the at-rest observer would be a tiny fraction, but somehow the space it has to travel for the moving observer is smaller by essentially the same amount so that it wouldn't ever reach lightspeed to an outside observer but the speed it did "gain" would basically be enough to propel it through the reduced amount of space of the moving observer at a speed that would seem to be as fast as a gun normally fires to him. Am I way of, or?

[Mordred]

Actually not bad.

 

If you model spacetime as coordinate points. 4d.

 

Time dilation and length contraction both occur. ( Time being the fourth coordinate.)

 

So when you involve length contraction, from coordinate to coordinate the velocity doesn't change. What changes is the number of coordinates from a to b. (Sort of, this is where terms such as spacetime stretches etc come from).

I'm going to cheat a bit on latex effort and use a previous post to help describe the above.

 

 

Lorentz transformation.

First two postulates.

1) the results of movement in different frames must be identical

2) light travels by a constant speed c in a vacuum in all frames.

Consider 2 linear axes x (moving with constant velocity and [latex]\acute{x}[/latex] (at rest) with x moving in constant velocity v in the positive [latex]\acute{x}[/latex] direction.

Time increments measured as a coordinate as dt and [latex]d\acute{t}[/latex] using two identical clocks. Neither [latex]dt,d\acute{t}[/latex] or [latex]dx,d\acute{x}[/latex] are invariant. They do not obey postulate 1.

A linear transformation between primed and unprimed coordinates above

in space time ds between two events is

[latex]ds^2=c^2t^2=c^2dt-dx^2=c^2\acute{t}^2-d\acute{x}^2[/latex]

Invoking speed of light postulate 2.

[latex]d\acute{x}=\gamma(dx-vdt), cd\acute{t}=\gamma cdt-\frac{dx}{c}[/latex]

Where [latex]\gamma=\frac{1}{\sqrt{1-(\frac{v}{c})^2}}[/latex]

Time dilation

dt=proper time ds=line element

since [latex]d\acute{t}^2=dt^2[/latex] is invariant.

an observer at rest records consecutive clock ticks seperated by space time interval [latex]dt=d\acute{t}[/latex] she receives clock ticks from the x direction separated by the time interval dt and the space interval dx=vdt.

[latex]dt=d\acute{t}^2=\sqrt{dt^2-\frac{dx^2}{c^2}}=\sqrt{1-(\frac{v}{c})^2}dt[/latex]

so the two inertial coordinate systems are related by the lorentz transformation

[latex]dt=\frac{d\acute{t}}{\sqrt{1-(\frac{v}{c})^2}}=\gamma d\acute{t}[/latex]

So the time interval dt is longer than interval [latex]d\acute{t}[/latex]

The above is what I would expect to see when one presents his own equation. The above isn't a full derivitave.

Several missing steps. It was for another post. However it provides a better explanation of the Lorentz transformations than merely posting a formula.

If your not using Lorentz then you need to define the coordinate transformation rules.

Here is relativity of simultaneaty coordinate transformation in Lorentz.

[latex]\acute{t}=\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}[/latex]

[latex]\acute{x}=\frac{x-vt}{\sqrt{1-v^2/c^2}}[/latex]

[latex]\acute{y}=y[/latex]

[latex]\acute{z}=z[/latex]

 

Now granted you may not understand the math above, but the velocity addition rules involve both length contraction and time dilation.

 

They go hand in hand. In a sense you can't seperate one from the other.

Edited April 8, 2016 by Mordred

[Eise]

Hypothetically, if you were on a ship that was travelling at just below c (for example 299792457,9 m/s) and you fired a gun at another person on that ship from where you were sitting in the direction that the ship was moving, what would happen?

 

You would kill that person, just as usual. You and the person are in the same inertial frame, so there is nothing special for you, the bullet, and the person.