What Happens When You Observe Objects While Traveling at Light Speed?

[phisci]

I was pondering about the following cases and I am wondering if gave a correct description for each case. Do tell me where I have gone wrong. Thanks!

Case 1:
When you travel near the speed of light and you observe a slow moving object. What do you see?
-The object appears squashed (in 1 direction?) Lorentz length contraction.

Case 2:
When you travel near the speed of light and you observe a photon. What do you see?
-The photon still travels at the speed of light.

Case 3: (Assume possible)
When you travel at the speed of light and you observe a slow moving object. What do you see?
- I am not too sure about this.

Case 4: (Assume possible)
When you travel at the speed of light and you observe a photon. What do you see?
-You’ll still see the photon moving off at the speed of light.

And i also would like to ask what are some of the invariant quantities in physics? So far I know that the 1.)spacetime interval, 2.)speed of light, 3.)mass. Did I miss out anything?

Thanks alot! :)

 

[bcrowell]

It's not necessary to think in terms of both the observer's velocity and the velocity of the thing being observed. All you need to talk about is the relative velocity. In case 1, the only thing that is relevant is the object's speed relative to you. In your frame, the object has a speed of, say, 0.9c, and you have a speed of 0. In the object's frame, it has a speed of 0 and you have a speed of 0.9c. In both cases, the relative velocity is 0.9c.

In case 1, the answer depends on what you mean by "see." If you mean visually observing, then actually the length contraction isn't what you see. You see a rotation and an expansion: http://en.wikipedia.org/wiki/Terrell_rotation

You have case 2 right.

Cases 3 and 4 are not possible, and there is no logically self-consistent way to get an answer by assuming they're possible. It's like saying, "Assume 2+2=5,..." More on this in the FAQ entry below.

FAQ: What does the world look like in a frame of reference moving at the speed of light?

This question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers.

The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light.

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)

What if a system of interacting, massless particles was conscious, and could make observations? The argument given in the preceding paragraph proves that this isn't possible, but let's be more explicit. There are two possibilities. The velocity V of the system's center of mass either moves at c, or it doesn't. If V=c, then all the particles are moving along parallel lines, and therefore they aren't interacting, can't perform computations, and can't be conscious. (This is also consistent with the fact that the proper time s of a particle moving at c is constant, ds=0.) If V is less than c, then the observer's frame of reference isn't moving at c. Either way, we don't get an observer moving at c.

 

[phisci]

Hi bcrowell, thanks for helping me clear up my misconceptions! I've got a clearer picture now. Thanks for taking your time to reply as well! One more thing on the invariant quantities in our universe. If I am not mistaken, they are the spacetime interval, speed of light, total mass and energy? Am I on the right track?

 

[bcrowell]

One more thing on the invariant quantities in our universe. If I am not mistaken, they are the spacetime interval, speed of light, total mass and energy? Am I on the right track?

Invariant and conserved are two different things. In SR, mass-energy is conserved but nor invariant, whille the spacetime interval is invariant but not conserved.

There is no conserved mass-energy scalar in general relativity.

Charge is probably conserved.

There are various conservation laws from particle physics, e.g., baryon number, that are not necessarily conserved in quantum gravity, e.g., in the evaporation of a black hole. (Wald has a good discussion of this.)

 

[Matterwave]

Invariant means that it takes the same value in different inertial reference frames. In this respect, the speed of light, space-time interval, and rest mass (sometimes called the invariant mass), are invariant. The energy is NOT invariant as it takes different values in different frames of reference.

 

[JesseM]

I think we should also distinguish between things which are invariant relative to inertial frames, like the speed of light, and things which are invariant relative to all possible coordinate systems, like proper time along a given worldline (the speed of light may be different than c in the coordinates of a non-inertial frame).

 

[Matterwave]

I don't know much about general relativity, so I wouldn't be able to distinguish between the two.

Interesting that the proper time is invariant but c is not in GR...does this mean that the interval is also no longer invariant since it is c*propertime, or is it that the interval is no longer c*propertime in GR?

 

[bcrowell]

I think we should also distinguish between things which are invariant relative to inertial frames, like the speed of light, and things which are invariant relative to all possible coordinate systems, like proper time along a given worldline (the speed of light may be different than c in the coordinates of a non-inertial frame).

Coordinates and frames are not the same thing. Coordinate velocities can be anything you like if you choose the arbitrary coordinates, so it's not surprising that the coordinate velocity of light isn't always the same number. A frame is a local thing in GR, not a global one. The speed of light is the same in all frames, including noninertial frames (because frames are local things, and the local speed of light does not depend on accleeration).

 

[JesseM]

Coordinates and frames are not the same thing. Coordinate velocities can be anything you like if you choose the arbitrary coordinates, so it's not surprising that the coordinate velocity of light isn't always the same number. A frame is a local thing in GR, not a global one. The speed of light is the same in all frames, including noninertial frames (because frames are local things, and the local speed of light does not depend on accleeration).

Are you sure this is agreed-upon terminology, or might it just be used by some authors? Do you have a reference that states this? Searching for "non inertial frame" +relativity on google books, there seem to be some books that talk about non-inertial frames in the context of general relativity (though many of the results just use the term in introductory discussions of Newtonian mechanics), see here and here and here and here for example.

 

[lugita15]

A frame is a local thing in GR, not a global one.

That's surprising. Does that mean that you can't "stitch together" local frames to make a global one? I guess you couldn't use inertial motion from one point to another because parallel transport is path-dependent on a curved manifold. But is there really no other way to get a global inertial frame?

 

[DrGreg]

JesseM and lugita15, I think bcrowell is using the word "frame" in the technical sense of a frame field, which means something different from a coordinate system (or chart).

(I'm no expert in this, I'm just recalling previous discussions.)

 

[lugita15]

JesseM and lugita15, I think bcrowell is using the word "frame" in the technical sense of a frame field, which means something different from a coordinate system (or chart).

(I'm no expert in this, I'm just recalling previous discussions.)

Is this the natural extension of the concept of an inertial frame to general relativity?

 

[GrayGhost]

In case 1, the answer depends on what you mean by "see." If you mean visually observing, then actually the length contraction isn't what you see. You see a rotation and an expansion: http://en.wikipedia.org/wiki/Terrell_rotation

bcrowell,

One thing that always perplexed me regarding the Terrell effect is that no one published a paper on this until 1959. I mean, I just don't see how anyone could have missed that for 50+ years. Anyone who glances at a Minkowski spacetime diagram portraying a moving rod can easily realize the Terrell effect. I have little doubt that Minkowski realized it. I figure that no one cared to bother with it, until Terrell (and Penrose).

GrayGhost