# Pushing in the wrong direction

1. Jun 23, 2008

### A.I.

Every time I come across a discussion of general or special relativity in school or around town, people are usually discussing the idea of moving at speeds that are close to the speed of light. This brought me to a slightly strange question regarding relativity:
Well... two...three questions:
We are, as a satelite around our sun, galaxy, and universe, moving quite quickly through space. Does this imply that we are currently more massive than we would be at some sort of absolute rest? Or is the mass of an object always gauged wiithin our own personal reference frame I.E. one moving at our own velocity with our own acceleration?
Secondly:
What would the implications be of having a negative speed?
And thirdly:
What would an object's attributes be if it were already (and had always been) traveling faster than light? I'm not trying to say it got there from any point slower than light. Let's just say it was created traveling at 1.5c m/s and ahs been that way since the beginning of time.

2. Jun 23, 2008

### tiny-tim

Hi A.I.!

The mass of an object is gauged within the personal frame of whoever is the observer.

If we're observing ourselves, then yes, our mass is our rest mass.
No implications at all … a negative speed in one direction is a positive speed in the opposite direction.

Mass (and some other things) only depends on the square of the speed, so being "negative" makes no difference.
Then all observers would agree that it was faster than light.

The closer it got to the speed of light, the larger its mass would be.

And it could never reach the speed of light, nor be slowed down slower than light

But if it could cause things, some observers would see it break the laws of causation.

3. Jun 23, 2008

### MeJennifer

A velocity can, in a given coordinate system, be negative but speed is always positive.

4. Jun 23, 2008

### yuiop

Perhaps it easier to see what is happening by substituting values of v into the gamma factor

$$1/\sqrt{1-v^2/c^2}$$

Assuming units such that c=1

For v = 0.8c the time dilation factor is 0.6

For v = -0.8c the time dilation factor is still 0.6. No change of sign because v is squared.

For v = 2c the time dilation factor is $$1/\sqrt{-1}$$

Since there is no "real" number multiplied by itself that gives a value of -1 we call that an imaginary result and normally that is an indication that the result does not have a physical reality.

The particle is experiencing imaginary time and has imaginary length, imaginary relativistic mass, imaginary momentum, imaginary energy etc. Father Christmas personally delvering Xmas presents to all the homes in the world in one night, has similar imaginary properties.

In short, Father Christmas, fairies and particles moving faster than the speed of light all belong in a set called "imaginary things".

5. Jun 23, 2008

### JesseM

You can make sense of many properties of tachyons if you assume they have an imaginary rest mass--see here. You can't talk about what time dilation or length contraction factors they'd experience, but then you can't really talk about such things for photons either, these notions only make sense for objects that have their own valid inertial rest frames as photons do not and tachyons could not (it's assumed in SR that the laws of physics work the same way in all valid inertial frames, but there would be no way to satisfy that requirement for a coordinate system where a photon or tachyon was at rest).

6. Jun 23, 2008

### yuiop

"However, tachyons are not entirely invisible. You can imagine that you might produce them in some exotic nuclear reaction. If they are charged, you could "see" them by detecting the Cherenkov light they produce as they speed away faster and faster. Such experiments have been done. So far, no tachyons have been found. Even neutral tachyons can scatter off normal matter with experimentally observable consequences. Again, no such tachyons have been found."

Imagine some collison in a accelerator where a tachyon particle is imagined to be emitted as result of the collision. THe tachyon can be imagined to traveling backwards in time. In other words the tachyon exists in the future where it has knowledge that the collison has occured even before the collision has occured in normal time and travels back in time in order to take part in the collison in the present when the collision actually occurs. That is a bit hard to swallow. It might however be a useful mathematical tool to think of it that way.

7. Jun 23, 2008

### A.I.

Haha! I never even imagined that there are laws of physics that actually govern santa's imaginary status!

As far as the negative speed, I may have been misunderstood-- or maybe I'm entirely off my rocker. All objects have some sort of vale for velocity which is a vector quantity, however I suppose I was wondering about a negative SPEED, which, now that I think about it is absolutely absurd to say.

I read some literature in which they used space-time diagrams to graph antiparticle and particle collisions (I believe anyway) something about particles changing to antiparticles and moving back and forth through time creating the illusion of particles beng created and destroyed entirely. I'll leave that for another discussion though, thank you all very much for your help.

8. Jun 23, 2008

### JesseM

I wasn't suggesting they are likely to exist, just the equations of relativity alone don't rule them out. Although FTL signals + the relativity of simultaneity would imply the possibility of sending information backwards in time, so as you say, that makes the existence of tachyons pretty hard to swallow.