to those who love physics...

[Scarlet Fever]

I need some discussion about a question I got in my Year 12 Physics book.

In 2025, a spaceship is traveling away from Earth at 2.0 x 10^8 m/s. At the same time, a spaceship from an alien solar system is traveling in the opposite direction at 2.5 x 10^8 m/s.

1. According to Newton's theories, what is the speed of the alien craft relative to the spaceship from Earth? [i got this part; 4.5 x 10^8 m/s]

2. Is this answer possible according to Einstein's theory of relativity?

The answers in the book say no, because it is greater than the speed of light.

That, I don't have a problem with; if it takes infinite force to accelerate a particle to the speed of light, it's not possible to get faster than the speed of light, as you would need more than infinite force to get that fast.

But neither of the objects are actually going at the speed of light; one just appears to be going that fast from the other. If you point two torches at each other and turn them on, the relative speed of light coming from one torch relative to the other would be twice the speed of light, which is apparently not possible.

What do you think?

 

[adrianblaine]

I think I agree with you (although it's been 4 years since my last physics class). It makes sense that the speed itself is greater than the speed of light, but like you said, nothing is actually going that fast, it is just a number.

EDIT: after reading other posts here, you should probably disregard my advice

 

[4409723]

I need some discussion about a question I got in my Year 12 Physics book.

But neither of the objects are actually going at the speed of light; one just appears to be going that fast from the other.

I think that's where your problem understanding begins. EVERYTHING is relative, who is to say that our view of the universe, sitting at the point that these two objects pass is any more 'valid' than either of the two objects. Also, who is to say that these one of these objects isn't stationary and your viewpoint and the other object are the moving at the speed of light. I believe that's the reason that ever recording a speed greater than light is not possible.

I'm no physicist but I did have two years of higher physics and we covered relativity for about two months.

 

[dobbin]

Its not possible. This is the whole point of Einstein's theory of relativity. You cannot simply 'add' the two speeds as you would if you were calculating the relative speed of two cars at much lower speeds. When dealing with things that are approaching the speed of light you have to use Einsteins theories to calculate the relative speed, which I think in this case will be very close to, but not quite, the speed of light.

(Its a long time since I studied this. In fact I gave up on maths and physics after my first year at university for this reason. Most of what I had learned for the previous 18 years was being shown to be wrong! As I was happy to stick with the old version of what I knew and understood, I changed and studied something else instead.)

 

[ruZZ.il]

take a look at this ,it'll show you how to calculate relative speeds on a 'parallel' line.. google around for lorentz transformations they are pretty nifty.. they enable you to calculate time and length dilations and the effects on mass..
(since your velocities are in a different direction, just use the negative value for one of them..)

 

[RacerX]

But neither of the objects are actually going at the speed of light; one just appears to be going that fast from the other. If you point two torches at each other and turn them on, the relative speed of light coming from one torch relative to the other would be twice the speed of light, which is apparently not possible.

It is not possible to move faster than the speed of light relative to anything else... that is why relativistic effects such as time dilation occur.

If you were able to sit on one of those photons and measured the relative speed of the photons heading towards you, you would get 3x10^8 m/s. If the light beams were pointed away from each other, and you again did the same experiment (sitting on one of the photons) you would again measure that speed of those photons moving in the opposite direction as 3x10^8 m/s relative to you.


To take all this much further than your text does...

If you do have two objects that move away from each other at faster than the speed of light, the space between them starts to brake down creating a boundary between them similar to that of the event horizon around a black hole.

Think of it this way, as the two objects increase in relative speed, they also increase in relative mass... that mass distorts space-time. If enough energy is there to exceed the (relative) speed of light, space-time starts to give way between them.

This effect is part of the inflation cosmology theory, and the out come is the creation of matter from the gravitational tidal forces (similar to Hawking radiation from the event horizon of a black hole).

 

[mduser63]

IIRC (been a while since I was in physics), while the speed of the spaceships relative to each other can't exceed c, it's fine for an observer on earth to say that their speed relative to each other (that is the speed at which the gap between them closes) from his point of view is greater than c, because neither one is going greater than c relative to him. Of course, the question asked for their speed relative to each other as observed from one of the ships...

 

[ruZZ.il]

actually, if you were sitting on one of those photons you'd see the speed of other photons to be zero. the speed of everything would be zero too.. simply cause your time dilation would be so extreem, that nothing would move.. not even you.. you'd be stuck in a frame of time. but if you'd slowly accelerate and try get to the speed of light.. youd never get there either.. your mass would increase more and more that you'd need more and more force to accelerate you.. preventing you to ever go 'that' fast.. if you tried this for a couple hours though, you may come back to find a very dusty house.. and a couple dead old friends.. again, the math may be a little complicated.. but google around for this stuff.. I've seen some cool animations around...

 

[RacerX]

actually... again, the math may be a little complicated.. but google around for this stuff.. I've seen some cool animations around...

Actually, if you find the math complicated, then I'm not surprised that you would be having problems with the example I gave.



And somehow I really doubt that googling will provide anywhere near the amount of information that 6 years* of upper division and graduate level mathematics and physics courses on this subject have provided me.




* Note: The 6 years would be end to end (one course right after the other, rather than a number of courses at the same time), and only on subjects that directly relate to relativity theory and the mathematics used (like Classical Differential Geometry, Calculus on Manifolds, Differentiable Manifolds, Riemannian Geometry and Integration on Manifolds).

 

[ruZZ.il]

ah, if I'd say i truly understood I'd truly be a goon.. though the maths really are my problem. fortunatly i managed with the lorentz transformations and stuff.. I got passed first year by work of god.. or me.. anyway, was just meaning that when the question is merely 'is it possible or not'.. there are fun animations out there to give a bit of a feeling for it.. an equation that shows how to add relatavistic velocities.. and a bunch of ppl still pondering this stuff to show you that if you dont quiet get it.. its still ok. (I hope...) now.. I wouldn't mind bending the space time continuum.. but I need to find my sword.

 

[RacerX]

ah, if I'd say i truly understood I'd truly be a goon..

Well, lets look at what you said...

simply cause your time dilation would be so extreem, that nothing would move.. not even you.. you'd be stuck in a frame of time.​

The dilation is of a nature that you wouldn't be aware that nothing was happening... that is the point. The dilation needs to be that extreme to make sure that even when you are traveling at the speed of light, the speed of light appears the same.

This is the very thought experiment that Einstein used when he first saw his math professor's* transformation developed to help resolve the results of the Madison-Morley experiment.

It is one thing to know that time dilation occurs, what you need for a true understanding is why time dilation has to occur. Similarly, distance dilation also has to occur because no matter what direction the photons are moving in relative to an observer's frame, the measured speed has to be the speed of light.

These effects aren't just curiosities, they are fundamentally important when you realize that the universe has no fixed reference frame. All reference frames are normalized by one constant... the speed of light.

Once you understand that... well, you'll finally be a goon I guess.



* Note: Lorentz was one of Einstein's professors, and while he was willing to put forward a mathematical explanation for the Madison-Morley results, he wasn't willing to go as far as Einstein was to make the speed of light the only real constant.

 

[maceleven]

Do you really plan on flying soon?