Traveling faster than the speed of light?

[maxwilli06]

This is technically referred to as the http://en.wikipedia.org/wiki/Tests_of_general_relativity#Perihelion_precession_of_Mercury". Mercury's orbit around the sun is approximately a circle, right? Really an ellipse.

With classical physics astronomers can calculate exactly how big the ellipse that Mercury traces around the sun with its orbit should be based on the masses of the sun and other planets and the force of gravity calculated based upon those masses. But because of the general relativity effects the immense mass of the sun actually shrinks the space around it, something like the length contraction effect from near-c speeds. So the circumference of the ellipse - the distance that Mercury has to go to make one orbit around the sun - is slightly shorter than it should be and so Mercury moves in a sort of corkscrew or http://en.wikipedia.org/wiki/Hypotrochoid" pattern.

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So the more gravity there is, the more space and time are bent? and if they are are they bent unanimously? I guess this gets into the other part of general relativity. I'm trying to figure out how gravity bends time. and at what point does it stop time completely.

 

[CaptainQuasar]

So the more gravity there is, the more space and time are bent?

Yes…

and if they are are they bent unanimously?

…but I don't get what you mean by that.

I'm trying to figure out how gravity bends time. and at what point does it stop time completely.

I don't know exactly how gravity does it. I know that merely describing the precise way in which gravity bends space and time involves something called tensor calculus. Tensor calculus is some sort of unholy miscegenation of multivariable calculus and matrix algebra. Just thinking about that gives me the willies.

As far as stopping time, I think you start to run into something like that with black holes.

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[tiny-tim]

change in frequency

If an object is moving next to a beam of light, it seems as though the faster you move, the easier it is to see individual photons (which is obviously not true). … Now if the same object is traveling against a beam of light, it seems as though it would be harder to pick out individual photons( also not true.)

Actually, it is true! If you move in the same direction as a beam of light (in other words, away from the source), then it is easier to see individual photons - a flashing light will appear to flash slower. Similarly, the wavelength will become longer, the frequency will be lower, and the light will be redder ("red-shifted"), and you will say that the light has lost energy.[/color]

If you move in the opposite direction, it is harder to pick out individual photons (they come "thicker and faster"), and so a flashing light will appear to flash faster, the frequency will be higher, and similarly the light will be blue-shifted, and you will say that the light has gained energy.[/color]

If you relative to any object, you will notice a change in its energy.

For a slower-than-light object, this change in energy is mostly because of the change in its speed, and only slightly because of an apparent internal effect, which we choose to call an "change in mass".

But, for light itself, there is no change in its speed, and so the change in energy is entirely because of an apparent internal effect, which we choose to call a "change in frequency (or colour)".

Light stays the same speed, but[/color] changes[/color] colour[/color].

However, since the speed of the beam is constant in relation to any reference frame, time has to compensate by slowing down the object's time in order to keep light moving at the constant speed. Meaning the faster you move, the more time has the compensate by slowing down, meaning the quicker you travel into the future.

Yes, but this has nothing to do with whether there happens to be some light going past you. You could have light going past you in two opposite directions, and yet you only have one clock! Your time "slowing down" has nothing to do with your speed or direction relative to light, but only relative to whoever is watching you and saying "ooh look, his time has slowed down!"

 

[Magnetron]

Faster than Light

Now I know no object object as yet observed by science can move faster that the speed of light (SOL), you did a very good job of explaining that.

But what would happen if we could see a spaceship moving faster than light?

Lets say we have a telescope that can see a spaceship traveling between two stars 10 light years away and that we, the observers, are on Earth directly between the stars but not quite (Just enough room for the ship to pass by us). Let's say this ship moves so fast that it only takes a few minutes to get from one star to the other.

Ive been racking my brain of what it would look like. If I am thinking correctly if the object goes from a distant star to the Earth, the spacecraft would beat its own light beams from when it was at the star. When the ship reaches us it would seem to just appear but simutaniously we would see the ship moving backward twards the first star, forwards twards the second star, and if the ship were in orbit around the first star being constructed for many years we would see that image too, all three images of the same thing at the same time. After the ship passes us It would just seem to be moving very fast away from us until it reached the second star.

Is this right?
I know the image of an object approaching the SOL is squished but what about those moving faster than the SOL?
What happens when the image of the ship traveling backwards twards the 1st star meets the image of the ship just before it leaves the star? Does it just disappear?
And what do we observe as the ship accelerates above the SOL, and then decelerates below the SOL?

 

[tiny-tim]

Welcome to PF!

{snip} When the ship reaches us it would seem to just appear but simutaniously we would see the ship moving backward twards the first star, forwards twards the second star, and if the ship were in orbit around the first star being constructed for many years we would see that image too, all three images of the same thing at the same time. {snip}

Hi Magnetron! Welcome to PF!

Everything you describe (which sounds about right) is an optical illusion, rather like looking at something moving past a warped mirror, and seeing two images of it appear out of nothing in the middle of the mirror, and move apart!

But in relativity (and in reality), we compensate for the speed of light being finite.

When we look at a distant star or galaxy, we are well aware that we are "looking at the past", and we make allowance for that in deciding what is the time of whatever we are looking at.

So when we see your spaceship appear from nowhere, and then move both forward and backward, it doesn't bother us … we know it's only an illlusion, which doesn't affect our maths!

 

[Mentz114]

Magnetron:

Now I know no object object as yet observed by science can move faster that the speed of light (SOL), you did a very good job of explaining that.

It isn't just a case of observation - if an object were to move at LS relative to us, any light from it would be red-shifted to nothing so we could not see it in principle.

And what do we observe as the ship accelerates above the SOL, and then decelerates below the SOL?

According to special relativity this absolutely cannot happen. If you had nearly infinitely powerful rocket engines you can get closer and closer to LS, but never reach it. And this is true from every observers point of view.

 

[tiny-tim]

It isn't just a case of observation - if an object were to move at LS relative to us, any light from it would be red-shifted to nothing so we could not see it in principle.

Hi Mentz114!

But wouldn't we be able to see it against the background?

If we were slightly offset from its track, it would hide light coming from distant stars, so we could tell, visually, where it was, and when?

According to special relativity this absolutely cannot happen. If you had nearly infinitely powerful rocket engines you can get closer and closer to LS, but never reach it. And this is true from every observers point of view.

Yes. STL has to stay STL. FTL has to stay FTL. No crossing LS.

 

[JesseM]

The relativistic doppler shift formula is for a source that's emitting radiation at some set frequency in its own rest frame--the reason redshift goes to infinity (i.e. frequency goes to zero) as you approach c is because of time dilation, so if the source is emitting peaks at a frequency of one peak/microsecond in its own frame, in our frame the time between peaks being emitted (not seen) gets longer and longer as the source approaches c, since the time between microseconds on a clock moving along with the object is getting longer in our frame because of time dilation. I'm pretty sure the doppler shift formula doesn't imply that the frequency of light which is reflected off a moving object must go to zero as its speed approaches c (for example, assume the frequency of the incoming light before it hits the object is held constant in our frame, and only the speed of the object is varied).

 

[Mentz114]

tiny-tim:

But wouldn't we be able to see it against the background?

If we were slightly offset from its track, it would hide light coming from distant stars, so we could tell, visually, where it was, and when?

Very likely. I don't see why it shouldn't cast a shadow.

I should add that my remarks about red-shift only apply to receeding sources.

JesseM:

the doppler shift formula doesn't imply that the frequency of light which is reflected off a moving object

Isn't reflected light being absorbed and re-emitted ?
Interesting point. How do doppler speed traps work ? I thought the velocity of the car changed the frequency of pulses.

 

[Hernik]

But what would happen if we could see a spaceship moving faster than light?

According to SR an object moving at the speed of light travels an infinite distance at 0 time. (That is maybe what light "experiences".) So who needs to go any faster than c?

I've seen considerations that anything going faster than c would be traveling backwards in time. Tachyons are believed to go that fast ... but no one has found a tachyon

- Henrik

 

[Hernik]

sorry.. this was an old dead end I just revived. Realized that too late.

 

[Austin0]

The relativistic doppler shift formula is for a source that's emitting radiation at some set frequency in its own rest frame--the reason redshift goes to infinity (i.e. frequency goes to zero) as you approach c is because of time dilation, so if the source is emitting peaks at a frequency of one peak/microsecond in its own frame, in our frame the time between peaks being emitted (not seen) gets longer and longer as the source approaches c, since the time between microseconds on a clock moving along with the object is getting longer in our frame because of time dilation. I'm pretty sure the doppler shift formula doesn't imply that the frequency of light which is reflected off a moving object must go to zero as its speed approaches c (for example, assume the frequency of the incoming light before it hits the object is held constant in our frame, and only the speed of the object is varied).

Hi You may of course be right about reflected light but it also appears that there is some reason to assume the opposite.
Whether or not you consider reflection to be a re-emmission or a direct reflected waveform , wouldn't both cases suggest the doppler effect would take place.
If the reflecting surface is moving in the time between the incidence of phase peaks, wouldn't this result in an expansion of the waveform [or contraction depending on direction of motion] of the reflected wave??
If it is a case of re-emmission , then the light would seem to be subject to the normal doppler shift ?

 

[JesseM]

Hi You may of course be right about reflected light but it also appears that there is some reason to assume the opposite.
Whether or not you consider reflection to be a re-emmission or a direct reflected waveform , wouldn't both cases suggest the doppler effect would take place.
If the reflecting surface is moving in the time between the incidence of phase peaks, wouldn't this result in an expansion of the waveform [or contraction depending on direction of motion] of the reflected wave??
If it is a case of re-emmission , then the light would seem to be subject to the normal doppler shift ?

Yes, you're right, even in the case of reflection the peaks would get shifted because immediately after one peak is reflected, then the next peak won't be reflected until it catches up with the object which is moving away from it, so the space between peaks will be greater than if the wave had been reflected by an object at rest in our frame. Although unless I'm thinking about it wrong, it seems to me like the shift would not be the same as the relativistic Doppler shift in this case, since time dilation doesn't seem to play any role--you can calculate the shift without worrying about multiple frames, so it's just a matter of kinematics your own frame and the shift shouldn't be any different than for a wave moving at c reflected off a moving object in classical physics.

 

[Austin0]

Yes, you're right, even in the case of reflection the peaks would get shifted because immediately after one peak is reflected, then the next peak won't be reflected until it catches up with the object which is moving away from it, so the space between peaks will be greater than if the wave had been reflected by an object at rest in our frame. Although unless I'm thinking about it wrong, it seems to me like the shift would not be the same as the relativistic Doppler shift in this case, since time dilation doesn't seem to play any role--you can calculate the shift without worrying about multiple frames, so it's just a matter of kinematics your own frame and the shift shouldn't be any different than for a wave moving at c reflected off a moving object in classical physics.

Actually you have touched on something I have been wondering about.
Does time dilation play a role in relativistic doppler shift?
It seems like the effect is a direct result of relative velocity and as such, the difference between approach and recessional velocities is equal and opposite, whereas the time dilation would be exactly the same in both cases.
Does it consider time dilation regarding electron resonance frequencies and the effect on emitted and absorbed frequencies which apply in GR , but wouldn't really make any sense in this context where the dilation is assumed to be reciprocal at emitter and receiver?
But then I am still having a hard time forming a consistent picture of the analogous situation in GR, where there are two different effects, the time dilation effecting the emission and reception electrons, and the frequency shift attributed to the photon translation though the gravitational gradient. Either one separately makes sense and seems to completely explain the observed phenomena , but taken together, it seems like one effect too many, unless the actual measurements were greater than expected for either one by itself.
If that makes any sense??
Thanks