Physics Question

lurrrvs2sp00ge

If im standing on top of a moving train at the front goin 100 kmph, for argument sake, and i shoot a gun the same direction as the train and the bullet has an acceleration of 100 kmph will the bullet stay in the gun because the gun is also moving 100 kmph or will the speed of the bullet increase and move ahead

For the record im not testing you i dont know the answer to this

Podge_irl

lurrrvs2sp00ge wrote: »

If im standing on top of a moving train at the front goin 100 kmph, for argument sake, and i shoot a gun the same direction as the train and the bullet has an acceleration of 100 kmph will the bullet stay in the gun because the gun is also moving 100 kmph or will the speed of the bullet increase and move ahead

100 kmph is a speed, not an acceleration.

The bullet will leave the gun at 100kph regardless of the speed the gun is moving (up to special relativistic speeds, but I think we can safely ignore them in this scenario). The bullet will thus be travelling at 200kph with respect to the ground.

Thumpette

Ha- nice question I like it!

My first instict was that it was a bit of a silly question- and that obviously the bullet would shoot out ahead, but then I was thinking it doesnt rwally matter to the bullet whether it is shot from a moving or stationary point.

The instant the trigger is pulled is the stationary point it leaves from, so I guess its possuble it doesnt move... but it must...but how...agh!

Could someone put us out of our misery on this one!:o

I imagine the bullet would travel out of the barrel with it's normal acceleration, as velocity is completely relative - i.e. To somebody stationary beside the train, the bullet would appear to be travelling at 200km/h. Air resistance would play a large role in the scenario, but if you disregard it, then I think that I'm correct.

For example, on Earth we're travelling around the sun at however many thousand km/h. But, if we fire a bullet on Earth it's still observed to travel at the velocity we predicted. But if we measure the velocity of the bullet from another reference frame - i.e. the sun - then we measure it to be travelling with it's own velocity + the velocity of the Earth (If the bullet is fired in the direction the Earth is travelling).

Anyway, to answer your question - If air resistance is disregarded, then I believe the bullet would travel at 100km/h relative to you, on the train (i.e. 200km/h relative to a "stationary" point).

Professor_Fink

Yes, as everyone else has said, the bullet shoots forward from the gun. You did give a velocity rather than an acceleration, which is causing some confusion. basically you need to either give the muzzle velocity, or the acceleration and time for which the bullet is accelerating (it stops accelerating when it leaves the barrel). Let's assume you mean the muzzle velocity is 100km/h. In that case by definition the bullet is moving at 100km/h relative to the gun and so 200kmp/h relative to the ground (actually special relative would make this a tiny bit less than 200km/h). So that case is easy. In the second case, if you are actually giving acceleration, then again the bullet leaves the gun, since acceleration is defined in terms of a change in velocities, not in terms of some absolute velocity.

lurrrvs2sp00ge

well seems like iv asked the rite people for this thanks guys

lurrrvs2sp00ge

lurrrvs2sp00ge wrote: »

well seems like iv asked the rite people for this thanks guys

A somewhat related and far more interesting question, one that goes against all logic is this (I'm sure most of you have heard it before):

If you're in a "car" travelling at 99.999% of the speed of light, c, and you turn on your headlights, what will happen? Will light radiate the "road" in front of you? Or will it remain "trapped" in the headlights? I know what the answer is, but I think it's an interesting question for someone who is thinking about relative velocities - i.e. like your original question.

Professor_Fink

-JammyDodger- wrote: »

A somewhat related and far more interesting question, one that goes against all logic is this (I'm sure most of you have heard it before):

If you're in a "car" travelling at 99.999% of the speed of light, c, and you turn on your headlights, what will happen? Will light radiate the "road" in front of you? Or will it remain "trapped" in the headlights? I know what the answer is, but I think it's an interesting question for someone who is thinking about relative velocities - i.e. like your original question.

Actually, I think you may have it wrong. There isn't really a definitive answer for this, since it depends on the observers reference frame.

Professor_Fink

Professor_Fink wrote: »

Actually, I think you may have it wrong. There isn't really a definitive answer for this, since it depends on the observers reference frame.

Oh I know I don't have a definitive answer, and I know there isn't one. My question is based on the following presumptions/reference frames. Would it be correct to take as the reference frames:

1) The car.
2) A frame where, when the velocity of the car is measured, it is measured to be 99.999% of c. (I'm not being terrible specific, but, a frame where initally, before the car accelerated to 99.999% of c, the car and the external observer had zero velocity relative to each other.).

Or are my reference frames completely wrong?

Professor_Fink

They're fine. I was just worried you were implying that there was a frame independant answer. But for the frames you picked you get two very different answers, so I withdraw my warning :-)

Ah that's ok, thanks for clearing that up! I wouldn't be quite the relativity expert that most of the contributors around here would be!

carlrac

Surely this is the same as the gun on the train? Even if the car is travelling at c (3x10^8m/s for those who care...) the light will still be emitted from the headlights at it's normal speed.
This is, of course, only if the car is powered by a flux capacitor. Obviously :rolleyes:

Michael Collins

carlrac wrote: »

Surely this is the same as the gun on the train? Even if the car is travelling at c (3x10^8m/s for those who care...) the light will still be emitted from the headlights at its normal speed.

If a person on the ground saw the bullet mentioned above, they would see it travelling at (almost) 200 km/h. But if someone measured the speed of the light which reached them from the train, they would find it would be c, not c + 100 km/h, that's the point.

Decerto

carlrac wrote: »

Surely this is the same as the gun on the train? Even if the car is travelling at c (3x10^8m/s for those who care...) the light will still be emitted from the headlights at it's normal speed.
This is, of course, only if the car is powered by a flux capacitor. Obviously :rolleyes:

not really a fact as no one knows what happens at c and if a photon was emmited from something moving at c it means by definition of it being emmited it would have to travel at faster then c to move from its source which is impossible

Decerto

Decerto wrote: »

not really a fact as no one knows what happens at c and if a photon was emmited from something moving at c it means by definition of it being emmited it would have to travel at faster then c to move from its source which is impossible

No, that's incorrect. If a massive object was moving at 99.99999999999% of c (it's impossible for a massive object to travel at c; so we'll say it's travelling arbitrarily close to c) and it emitted a photon, that photons velocity relative to the massive object would be measured as c. Now, if another observer measured the same photon from a "stationary" point, they would also measure the photon to be travelling at c.

Decerto

it was hypothetically speaking, if something was moving at c not near it like carlrac said,

Decerto

Decerto wrote: »

it was hypothetically speaking, if something was moving at c not near it like carlrac said,

Yah I suppose so. But, I consider it to be an answerless question. It's like asking "what happens if I walk to the north pole, then go north a bit more". It's a logical impossibility to answer it - with the current theory, that is.

Decerto

-JammyDodger- wrote: »

Yah I suppose so. But, I consider it to be an answerless question. It's like asking "what happens if I walk to the north pole, then go north a bit more". It's a logical impossibility to answer it - with the current theory, that is.

well since our belief at the moment is that no particles can move faster then c, his statement about light being emitted from something moving at c is false, it just physically cant be emitted, but like you said anything with mass cant reach c and photons are fundamental particles so they cant emit anything so the situation is completely impossible to create unless someone gets cracking on one of those flux capacitors

JoeB-

Here's one I just thought of...

What if some light is bouncing between two mirrors?, and we are travelling in one direction at .5c say... So the light is travelling with us when it goes in one direction, then it reflects off a mirror and goes in the opposite direction to us, (then it reflects again and goes in our direction etc).

So what do we see (travelling by at .5c)?

The light must appear to us to be going at exactly c no matter what direction it is travelling in... and so the apparent lengths must change to accomadate this.. BUT the lengths are the same!!!, as the light is bouncing BETWEEN two mirrors! He he.

So the distance between the mirrors can't get longer when we measure light in one direction,and shorter when we measure it in another.

So what would really happen?

I'm not sure I understand your question fully Joe.

Would the mirrors be held to our side; Or infront/behind us - i.e. Would each mirror be perpendicular to the direction of travel? Or would they be parallel?

If they're parallel to the direction of travel, then I don't see any issues arising out of it. The light and mirrors would basically just behave as if they were standing still.

But, if the mirrors are perpendicular to the direction of travel, things would be different (but you wouldn't notice that they are, because the same factors affecting the beam and mirrors are affecting you). The faster something massive goes, the shorter it becomes in the direction of travel. So, at relativistic speeds (those approaching the speed of light) things become shorter and shorter (but only along the axis in the direction of travel, their dimensions remain the same in both other axes). So in essence, relative to a "stationary" point, the distance between the two mirrors has decreased. But, basically, if you measured the speed of the beam, you'd still find that it's c at all times; It doesn't matter if it's coming towards you, or away from you. This has to do with length contraction and time dilation etc.

I probably didn't explain that very well as I didn't fully understand your question. If I didn't just repost and clarify!

Professor_Fink

Decerto wrote: »

not really a fact as no one knows what happens at c and if a photon was emmited from something moving at c it means by definition of it being emmited it would have to travel at faster then c to move from its source which is impossible

JammyDodger is right. It's also incorrect to say noone knows what happens at c. We do, but the only thing that travel at c are massless particles (which necessarily travel at c). The issue here is that accoring to special relativity velocities do not add linearly, but rather according to the formula w = (u+v)/(1 + uv/c^2), where u and v are the velocities to be added (i.e. the velocity observed in frame F and the velocity of frame F relative to the new frame F'). Since light if fast (3*10^8 m/s), for the train example uv/c^2 is miniscule, so the velocities add very close to linearly. This is always true when u or v is much less than c. Even if you are dealing with speeds of 10% the speed of light, the special relativity correction is very small.

In the example of the car and the headlights the corrections get very big. If we use v=c as in the example, then w=(u+c)/(1+u/c) = c, so the speed of light is the same in both frames. This is actually the core assumption of special relativity, so it isn't surprising to see it popping back out. So in the rest frame of the road, the car and the photons are moving at very similar speeds, with the photons essentially staying very close to the headlights. In the rest frame of the car, the photos race off at c.

Professor_Fink

JoeBallantine wrote: »

So what do we see (travelling by at .5c)?

See my other post. Light always travels at c relative to the observer.

Decerto

Professor_Fink wrote: »

JammyDodger is right. It's also incorrect to say noone knows what happens at c. We do, but the only thing that travel at c are massless particles (which necessarily travel at c). The issue here is that accoring to special relativity velocities do not add linearly, but rather according to the formula w = (u+v)/(1 + uv/c^2), where u and v are the velocities to be added (i.e. the velocity observed in frame F and the velocity of frame F relative to the new frame F'). Since light if fast (3*10^8 m/s), for the train example uv/c^2 is miniscule, so the velocities add very close to linearly. This is always true when u or v is much less than c. Even if you are dealing with speeds of 10% the speed of light, the special relativity correction is very small.

In the example of the car and the headlights the corrections get very big. If we use v=c as in the example, then w=(u+c)/(1+u/c) = c, so the speed of light is the same in both frames. This is actually the core assumption of special relativity, so it isn't surprising to see it popping back out. So in the rest frame of the road, the car and the photons are moving at very similar speeds, with the photons essentially staying very close to the headlights. In the rest frame of the car, the photos race off at c.

but from the rest frame of the road, is it not immposible for a photon to be emitted from the car since its moving at c, because if it is emitted forward then it would have to accelerate to above c to come out of its source

Decerto

Decerto wrote: »

but from the rest frame of the road, is it not immposible for a photon to be emitted from the car since its moving at c, because if it is emitted forward then it would have to accelerate to above c to come out of its source

The way I see it, you can't use an assumption of special relativity to answer a problem that directly contradicts one of its other assumptions (i.e. using special relativity to answer a problem about a massive object travelling at c; you can't - it's a contradiction).

Professor_Fink

Decerto wrote: »

but from the rest frame of the road, is it not immposible for a photon to be emitted from the car since its moving at c, because if it is emitted forward then it would have to accelerate to above c to come out of its source

Massive objects cannot move at c. If they could, the photon would never leave the headlight. Also, the analysis would be flawed for looking at the rest frame of the car, since there is no rest frame for light.

I've a somewhat related question about light, Professor_Fink, that you might be able to answer; because the terminology in anything decent that I've tried to read about it simply goes over my head.

You know how scientists have been able to stop a beam of light in a Bose-Einstein condensate? I understand the basic ideas behind what a Bose-Einstein condensate is etc. But, I don't understand what it is exactly that they're doing.

How do they know that they have it stopped? And is it that they are actually capturing an electro-magnetic vibration in the "fabric" of space? In what way are they actually stopping the light beam?

Thanks.

Professor_Fink

-JammyDodger- wrote: »

You know how scientists have been able to stop a beam of light in a Bose-Einstein condensate? I understand the basic ideas behind what a Bose-Einstein condensate is etc. But, I don't understand what it is exactly that they're doing.

How do they know that they have it stopped? And is it that they are actually capturing an electro-magnetic vibration in the "fabric" of space? In what way are they actually stopping the light beam?

Good question. All the comments I've made about the speed of light apply only to light in a vacuum. Basically they are transfering the state of the light to the BEC and back again, which essentially slows or stops the light. The photons themselves don't stop, they get absorbed and reemitted.

Professor_Fink

Professor_Fink wrote: »

Good question. All the comments I've made about the speed of light apply only to light in a vacuum. Basically they are transfering the state of the light to the BEC and back again, which essentially slows or stops the light. The photons themselves don't stop, they get absorbed and reemitted.

Ah right, that's what a presumed alright. So the BEC is just so dense that the photons are forced to be absorbed and re-emitted extremely frequently, basically? So they're technically not stopping a "beam" (I know beams don't technically exist) of light? They're just slowing the movement of the photons to an arbitrarily slow rate?

Professor_Fink

-JammyDodger- wrote: »

Ah right, that's what a presumed alright. So the BEC is just so dense that the photons are forced to be absorbed and re-emitted extremely frequently, basically? So they're technically not stopping a "beam" (I know beams don't technically exist) of light? They're just slowing the movement of the photons to an arbitrarily slow rate?

Eh, not exactly. It's not that the BEC is dense, just that they can drive certain transitions which cause the photon to be absorbed or emitted. It's based on electromagnetically induced transparancy. The wikipedia article on EIT should explain how this works better than I can in a post.

lurrrvs2sp00ge

i dont think i have any part in this thread anymore

Decerto

Professor_Fink wrote: »

Massive objects cannot move at c. If they could, the photon would never leave the headlight. Also, the analysis would be flawed for looking at the rest frame of the car, since there is no rest frame for light.

It was all hypothetical anyways like i said, because calrac asked the question + i know the basics of special rel or at least im supposed to after doing the course in college, ive got another question aswell about inertial ref frames, does the fact that since the earth is rotating and in orbit around the sun and the solar system is in orbit around the black hole at the centre and also since the universe is expanding not completely invalidate the idea of an inertial reference frame since everything is constantly accelerating or are these effects countered or neligible

Podge_irl

Decerto wrote: »

It was all hypothetical anyways like i said, because calrac asked the question + i know the basics of special rel or at least im supposed to after doing the course in college, ive got another question aswell about inertial ref frames, does the fact that since the earth is rotating and in orbit around the sun and the solar system is in orbit around the black hole at the centre and also since the universe is expanding not completely invalidate the idea of an inertial reference frame since everything is constantly accelerating or are these effects countered or neligible

It doesn't invalidate the idea of an inertial reference frame, it just means we're not in one. As far as I understand (and it wouldn't be a first if I was wrong) there is no actual inertial reference frame in the universe. But then you could equally say that SR is always incorrect since gravity is a long range force and you thus can't discount its effects. It provides a good approximation under the right conditions.

Decerto

Podge_irl wrote: »

It doesn't invalidate the idea of an inertial reference frame, it just means we're not in one. As far as I understand (and it wouldn't be a first if I was wrong) there is no actual inertial reference frame in the universe. But then you could equally say that SR is always incorrect since gravity is a long range force and you thus can't discount its effects. It provides a good approximation under the right conditions.

the amount of times ive heard that in physics

Professor_Fink

Decerto wrote: »

ive got another question aswell about inertial ref frames, does the fact that since the earth is rotating and in orbit around the sun and the solar system is in orbit around the black hole at the centre and also since the universe is expanding not completely invalidate the idea of an inertial reference frame since everything is constantly accelerating or are these effects countered or neligible

Well, the acceleration cancels the effect of gravity, so freely falling frames are inertial. Since the planet is in free fall, it constitutes an inertial frame. The local effect of gravity from the mass of the earth means we don't experience a truely intertial frame unless we do something like parabolic flight or go into orbit. On the other hand, the earth's gravity is so week it doesn't really change things.

General relativity is required to deal with regimes with strong gravitational fields.

Decerto

Decerto wrote: »

the amount of times ive heard that in physics

An intertial reference frame is basically just a frame where the laws of physics work in their simplest form. They don't hold in their simplest form around gravity because, for example, you'd have to take the force of gravity into account in your equations of motion etc.

But, as Professor Fink said, a free falling frame cancels out the force of gravity. So, that's inertial. Likewise, the shuttle orbiting earth "doesn't" feel the force of gravity, as it's in freefall, so that's an intertial frame of reference. Or at least they're as close as we can get!:pac:

carlrac

If nothing is faster than light, how come it can't escape a black hole?

Also, wasn't it scientifically accepted years and years ago that it was impossible to travel faster than the speed of sound!?

carlrac

carlrac wrote: »

If nothing is faster than light, how come it can't escape a black hole?

Without getting into too much detail, a blackholes gravity is so strong that light can't escape. It doesn't have anything to do with its speed.

Also, wasn't it scientifically accepted years and years ago that it was impossible to travel faster than the speed of sound!?

I'm not sure about that, perhaps it was. But, it's now accepted and proven mathematically that nothing with mass can travel at, or faster than, the speed of light. If something with mass travels at the speed of light it becomes infinitely massive, infinitely thin in the direction it's travelling, and time stops for the object.

pljudge321

carlrac wrote: »

If nothing is faster than light, how come it can't escape a black hole?

Also, wasn't it scientifically accepted years and years ago that it was impossible to travel faster than the speed of sound!?

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html

This page will answer pretty much any questions you could conceive.

Professor_Fink

carlrac wrote: »

If nothing is faster than light, how come it can't escape a black hole?

Well, every massive body has an escape velocity associated with it. For a black hole, the density is sufficient for the escape velocity to be c at the event horizon. Anything within it cannot escape, since nothing travels faster than c.

carlrac wrote: »

Also, wasn't it scientifically accepted years and years ago that it was impossible to travel faster than the speed of sound!?

No. We've had things that travel faster than the speed of sound for hundreds of years. The tip of a bull whip breaks the speed of sound (hence the crack). Some people thought it would be essentially impossible to engineer a plane to fly faster that the speed of sound, but that was a concern about engineering limitations, not what was fundamentally possible.

lurrrvs2sp00ge

eeemmmmmm, when did this stop being about the whole train and bullet thing

lurrrvs2sp00ge

lurrrvs2sp00ge wrote: »

eeemmmmmm, when did this stop being about the whole train and bullet thing

A long time ago!

I just thought of something interesting there. If a photon moving at c could be used as a frame of reference, would the entire universe be "destroyed"? Because now, relative to the photon, the entire universe is moving at c, so it'd have infinite mass and it'd be lorentz contracted to be infinitely thin in the direction the photon is moving, relative to the photon of course.

I know that this question is completely and absolutely theoretical. But, I suppose that's why a photon can't be used as a frame of reference, yah?

Professor_Fink

-JammyDodger- wrote: »

I just thought of something interesting there. If a photon moving at c could be used as a frame of reference, would the entire universe be "destroyed"? Because now, relative to the photon, the entire universe is moving at c, so it'd have infinite mass and it'd be lorentz contracted to be infinitely thin in the direction the photon is moving, relative to the photon of course.

Well, things aren't quite so simple, since a photon doesn't experience time or space (because of time dilation/length contraction), so it is meaningless to ask about energy, inertial mass, etc. You see the problem? You can't ask about dynamic properties if you don't have time.

Professor_Fink

Professor_Fink wrote: »

Well, things aren't quite so simple, since a photon doesn't experience time or space (because of time dilation/length contraction), so it is meaningless to ask about energy, inertial mass, etc. You see the problem? You can't ask about dynamic properties if you don't have time.

Ya, I get you. But, I always thought length contraction/time dilation just applied to massive objects? Does it apply to the photon as well?

Professor_Fink

-JammyDodger- wrote: »

Ya, I get you. But, I always thought length contraction/time dilation just applied to massive objects? Does it apply to the photon as well?

Length contraction is space contracting, not the specific object contracting, so in that context5 everything contracts.

Professor_Fink

Professor_Fink wrote: »

Length contraction is space contracting, not the specific object contracting, so in that context5 everything contracts.

I know these are pretty basic questions! But, does the space contract locally (I don't think that's it); or does the space everywhere contract relative to the photon (I'm afraid of saying relative to the photon, because it can't be used as a reference frame)?

Professor_Fink

-JammyDodger- wrote: »

I know these are pretty basic questions! But, does the space contract locally (I don't think that's it); or does the space everywhere contract relative to the photon (I'm afraid of saying relative to the photon, because it can't be used as a reference frame)?

I may have phrased my las response poorly, so let me try to explain what I mean. Imagine you have a collection of massive objects at rest relative to one another. As you approach the speed of light, the distance between the objects contracts in the direction of motion. At c, all these objects lie in the same plane since there can be no distance between them (in the direction of motion). This is true for all massive objects, so the photon basically is everywhere along the geodesic at once.

Professor_Fink

Professor_Fink wrote: »

I may have phrased my las response poorly, so let me try to explain what I mean. Imagine you have a collection of massive objects at rest relative to one another. As you approach the speed of light, the distance between the objects contracts in the direction of motion. At c, all these objects lie in the same plane since there can be no distance between them (in the direction of motion). This is true for all massive objects, so the photon basically is everywhere along the geodesic at once.

Ah I see, that makes it pretty clear. Any book recomendations about the consequences of SR, or indeed GR? If you know what I mean. I've attempted to read Gravitation by MTW, but, I'm stumped ~200 pages in; guess I'll have to wait until college to gain the relevant knowledge in maths.

timbrophy

-JammyDodger- wrote: »

Any book recomendations about the consequences of SR, or indeed GR?

I can highly recommend "Spacetime Physics" by Taylor and Wheeler as an introduction to SR. It does not shy away from Maths but anyone with Leaving Cert Higher Maths will have no trouble following it. GR does demand a much higher level of Maths but "Black Holes and Time Warps" by Kip S. Thorne does provide a very good introduction to GR without the Maths. You will understand GR after reading this book, you just will not have the mathematical equipment to analyse various scenarios. Remember that Einstein could not do the Maths himself, he had the ideas but needed help with the Maths.

Professor_Fink

There is a really nice really short book by Dirac on general relativity. Only costs a few quid, and is excellent, although not as gentle an introduction as it could be.

Thanks guys, I'll take a look into both.