# The Sophomore's Crack

1. Apr 19, 2004

### OneEye

Sohomore = Gk. Soph- (wise) + moros (fool).

I don't doubt that this question has been posited in this forum any number of times, and so I apologize if I am being a chore to anyone, but...

In response, the sophomore cracks: "Relative to what?"

How does the professor answer the sophomore?

2. Apr 19, 2004

### Staff: Mentor

3. Apr 19, 2004

### OneEye

Not going to directly gainsay your reference, but both Webster's and AHD support the etymology I gave.

In SR, velocity is a relation, not an inherent quality. In my own inertial frame, my velocity is always 0. If I may not exceed the speed of light, the question is, in relation to what may I not exceed the speed of light?

4. Apr 19, 2004

### jdavel

In relation to anyone who measures your speed.

5. Apr 19, 2004

### Staff: Mentor

I would think that velocity is always a relation, even pre-SR. In any case, the statement would be that no material object (including you) can exceed the speed of light with respect to any inertial frame.

6. Apr 19, 2004

### Dissident Dan

I think that the idea is that your time slows in comparison to another observer's. If you are only going 100 mph relative to me, your clock won't appear to have slowed down very much (probably not even measurable). However, relative to someone else, you may be going 0.3c, in which case you would appear to slow down appreciably. However, relative velocities should be symmetric, right? So, the observer should be going the same 0.3c compared to you, in which case he would have slowed down relative to you. How can you both slow down relative to each other?

7. Apr 19, 2004

### jdavel

Dissident Dan asked: "How can you both slow down relative to each other?"

Here's an analogy. Suppose you look at somebody through a big magnifying glass. He looks bigger to you. But you look bigger to him. How can that be?

8. Apr 19, 2004

### OneEye

Assuming I have this right: In a Newtonian context, there is a K0 coordinate frame with respect to which every other inertial frame is in motion, and a v0 "really" at rest. SR expressly denies any such concepts. This is precisely the innovation of Relativity: That no object can, in and of itself, be said to be "in motion" or "at rest."

So, then, if we could apply a simultaenous acceleration to every object in the universe such that every object was accelerated by .7c, then we have "upped the ante", and are now at liberty to accelerate any one object in the universe by (say) .4c relative to the rest of the universe, and this would be a legitimate velocity, even thought it is 1.1c WRT our original frame of reference? Or, perhaps, we could accelerate every object in the universe by .5c three times in a row. Now the entire universe is moving at 1.5c WRT the original condition, but there has been no contemporaneous change in relative velocity for any object in the universe. If such a process took place over a few billion years, who would be the wiser?

And another question comes to mind: Are we quite sure that no two objects in the entire universe have an aggregate relative velocity greater than c?

A third consideration: Imagine an empty, closed universe in which exists only a spacecraft with an impulse engine (http://chaos.fullerton.edu/~jimw/staif2000.pdf). The impulse engine is running, and has been running for an immeasurable period of time. The relative velocity of the craft is always 0, and yet the craft is experiencing a continuous acceleration from the impulse engine. (Or is it? In any case, energy is being expended, force is being applied, so one would expect that work was being performed). This is the conclusion that we reach if we say that the speed-of-light limitation applies only to an object's velocity relative to any other inertial frame. BUT, as soon as the spacecraft jettisons one pop can, the rules change, and the days of acceleration are numbered. Right?

So then, I don't think this is the right answer. But maybe someone can clear all this up for me.

Still puzzled.

Last edited by a moderator: Apr 19, 2004
9. Apr 19, 2004

### Staff: Mentor

...and in relation to whatever object you choose to measure your speed from.
What follows is Newtonian physics applied to a non-Newtonian situation. Sorry, OneEye, no, it just doesn't work that way.
Of course not - nor need we be. Thats why its important to understand what a "theory" is.
Again, you're applying Newtonian physics to a non-Newtonian situation. Sorry, OneEye, no, it just doesn't work that way.
Nothing at all changes for those inside the spacecraft from before to after the soda can is jettisoned. They still feel the same acceleration force.

10. Apr 20, 2004

### OneEye

I would like a little more elaboration on this, please. How am I applying Newtonian physics to a non-Newtonian situation? Is it because the velocities are very near light?

I am especially perplexed about the second model - the spaceship in the void. I cannot see the Newtonian aspects of this model - or rather, how the situation can be said to be either "Newtonian" or "Relativistic" - or why the consideration I posed can be said to invoke a Newtonian perspective.

A little help?

(And anyway, thanks for your time!)

11. Apr 20, 2004

### Staff: Mentor

I have no idea how one would accelerate every object in the universe (never mind simultaneously). But I think your point is: Can't one view relative velocities as additive? If ship B moves at 0.7c relative to ship A, and ship C moves at 0.7c relative to ship B, then doesn't ship C move at speed 1.4c relative to A?

The answer is no. Under SR, velocities do not simply add like they do under Newtonian physics.

12. Apr 20, 2004

### OneEye

$$W={ { v+w } \over { 1 + { vw \over c^2 } } }$$

The question is, if c is a limiting velocity, then what is that limiting velocity relative to?

The reason that I proposed those peculiar cases was to eliminate from the model every consideration of relational velocity.

It seems to me that we have three basic ways of intepreting the idea of c as a limiting velocity:

1) c is the limiting relative velocity in the universe - i.e., no two bodies in the universe can have a relative velocity greater than or equal to c.

2) no individual body in the universe can exceed c in and of itself. This second idea is, I think, incompatible with a foundational tenet of SR to the effect that all velocity is relative velocity.

3) Some other possibility which has not yet been mentioned. ()

If feel caught in no-man's land between relative and absolute velocity. Can anyone help me out of here?

13. Apr 20, 2004

Staff Emeritus
I think your option 1 is the prediction of relativity. Yes all velocity is relative and no relative velocity can be greater than c.

14. Apr 20, 2004

### Staff: Mentor

Yes, thats it exactly.
Unitil the can is released, its neither and either: it has no velocity, so while either can be used, neither tell us anything of value regarding velocity. You can certainly measure some forces of acceleration, but they don't tell you anything about your velocity.

Once you toss the can over the side, which situation you have depends on your velocity relative to the can. I don't know what would be considered the cutoff point (if any) where Einstein's is preferable.
...which we already told you is meaningless. All velocities are "relational" (relative).

So #1 is correct, #2 isn't so much wrong as it is meaningless.
Its simple but for some reason difficult to accept: "absolute velocity" quite simply does not exist.

Try this: how exactly would you measure "absolute velocity?" Distance over time? Where do you get the distance...?

15. Apr 20, 2004

### OneEye

Okay, but it occurs to me that if we want to avoid "spooky action at a distance," we are going to have to say that "c is the unattainable upper limit of relative velocity within any event cone". Right?

I didn't really intend to get into that particular question. It is obvious that the concept of absolute velocity is a stumblingblock over which those who study SR routinely trip. As I indicated, I am not suggesting that absolute velocity exists - especially without some proposal as to how to measure it.

I had thought of such a method based on Dr. Einstein's book: A given particle ought, theoretically, to have a given mass. Particle mass can be determined by the traces produced in a particle accelerator. The difference between the detected mass and the theoretical mass should tell us the "true" velocity of the particle directly, and will probably have a derivable component which tells us the velocity of the observer's inertial frame. However, someone on the board stated that the concept of "relativistic mass" had been jettisoned some time ago (even during Dr. Einstein's lifetime), so apparently this method is not effective.

Other than that, I can think of no obvious way to measure absolute velocity. So, I must conclude that, whether absolute velocity exists or not, it appears to be a concept of no value - unless someone can think of a way to measure it.

16. Apr 20, 2004

### turin

You do not need to toss a can out the window to realize that you are moving relative to something. Whince have you acquired the acceleration? Acceleration is not possible in the complete absense of any other bodies. I did not read that link about the impulse engine, but I did see extensive reference to Mach's principle, which hinges on the existence of some extraneous mass distribution (no other masses in the universe = trivialized Mach's principle).

In order to supply an impulse to the ship, something else in the universe must take on the negative of that impulse (conservation of momentum). Then, naturally, wrt this "something else" one can determine a velocity. This negative impulse could have been delivered to a soda can, to exhaust vapors, or even to photons. In any case, there is always something that provides a reference.

17. Apr 20, 2004

### OneEye

The link I provided was not for the impulse engine design I had in mind (and saw some years ago on the web). The design I was considering had a power unit, a tower proceeding from the unit, and a rotating arm assembly at the top of the tower. Power flowed to the rotating arm assembly, where it energized a coil at one exact position in the rotation of the arm (say, at the 0o position). The energy in the coil produced a transient effective mass, but only when the coil was in the specific orientation - thus causing an acceleration at the energizing angle.

I have no idea whether this would work or not. And that's not really the point. I was simply trying to provide a mental model which would allow investigation of the statement that "the velocity c plays the part of an unattainable limiting velocity."

HTH.

18. Apr 20, 2004

### turin

Just think about what you have to do in order to accelerate. You have to push on (off of) something. Whatever that something is cannot be pushed to a speed faster than c relative to you. Therefore, relative to it, you cannot push yourself to a speed faster than c. Then, for succesive pushes, the SR velocity addition formula kicks in.

19. Apr 20, 2004

### OneEye

All right, this gives us another window into the question:

I and my twin are flying through space together with atomic bombs strapped to our backs. We pass near a MACHO, against which we (my twin and I) have a relative velocity of .99c. I touch off my bomb, and it gives me a boost of .1c relative to my twin. Or does it? Does the presence of the MACHO in my event cone prevent me from gaining the velocity boost which I would otherwise have gained should the MACHO have not been nearby?

20. Apr 20, 2004

### Staff: Mentor

Why wouldn't it? Your speed with respect to some other observer (the MACHO, or whatever) is irrelevant.