# Interesting questions on relativity

1. Nov 23, 2004

### Gamish

Here are a few questions that I have built up. If someone knows the awsner to some of them, I would greatly appreteate your help.

1.If a "body" were to exceed c, then time would go in reverse for that body of motion, not time around them, right? For instance, let A travel faster than c, relevant to stationary observer B. Time for A would go in reverse, with respect to B then. I don't call this Time Travel to the past, unless I am incorrect. "If this were possible, one could be young forever, not bad :tongue2: "

2.Can an "internal" body of motion exceed c, with respect to the motion of a larger body that it lies within. For instance, lets say that the world's rotation, the the movement of our solar system, and the movement of the milky way added up to .6c. Then if we were to also reach .6c on earth, that would be 1.20c relevant to a stationary observer within the universe. Will the fabric of space-time allow such internal motion of exceed c?

4.If we were traveling at .99c, then time would significant decrease for us, but what if that craft we were traveling in generated a high gravitational fled, in which it warped space-time. So time would run slow because of the velocity near c, and the gravitational fled, and if I'm correct, this is a negative number. Would this allow time travel to the past?

5.The photon has no rest mass, yet, by means of it's own speed, it contains kinetic energy. If I'm correct, kinetic energy has mass, this means that something with mass is traveling at c. If this is indeed true, can the "photon" also carry matter, not just energy? And if it did, it should be hypothetically possible to reach c.

6.This question concerning time dilation and length contraction, in which I'm confused. If one reaches .6c, time and length will decrease by about 40% for a stationary observer, but will time and length LITERALLY decrease for the mover? For instance, I'm going .6c, time slows down by 40%, does time literally go slow for me, but I don't perceive it because even my brain waves are slow? Or does time LITERALLY run normal for me, but time runs fast around me? I'm just a little confused here. Because as I understand, the warping of time occurs only by the density of space IE if space is thick, time runs slower.

2. Nov 23, 2004

### Hurkyl

Staff Emeritus

1. Time does not slow down for anybody.

Belief to the contrary stems from the fact of time dilation naively blended with the Newtonian depiction of space-time.

What is true is that if we're moving (inertially) relative to each other, then I will observe my clock ticking faster than your clock.

However, you will also see your clock ticking faster than my clock.

If we're not moving inertially, things get more complicated, but can still be calculated through calculus and/or geometry.

The misconception stems from treating time as its own dimension, rather than part of a four dimensional space-time. We are already familiar with analogous examples of motion through space.

For example, suppose you and I start at the same place, and I plan to stroll north and you plan to stroll northeast.

After taking 100 steps, I pause and turn east to look at the point on your path, and see that it would take you 141 steps to reach that point.

However, after taking 100 steps, you pause and turn northwest to look at the point on my path, and you would see that it would take me 141 steps to reach that point.

Each of us finds that the other takes 41% more steps to cover the same distance because we're measuring in different directions -- I'm measuring northerly travel and you're measuring northeasterly travel.

Geometrically speaking, time dilation is exactly analogous to this; two observers in relative motion measure "coordinate time" along different directions in space-time, and thus see each other's clocks running at different rates. And as in this spatial example, it is still consistent for each of us to observe each other's clocks running slowly.

2. 0.6c + 0.6c = 1.2c

This is yet another holdover from the older notion that space and time are "separate". However, as in the previous section, things change once you accept a unified space-time. Here, the resolution is that these two relative velocity vectors don't point in the same direction. Thus, when you add them, their net length is not simply the sum of the individual lengths. The geometry of SR is such that adding vectors with lengths less than c will always yield another vector with length less than c.

3. Gravitational time dilation vs relativistic time dilation

Things like "time dilation" become less well defined once you step into GR -- talking about such things requires one to impose the idea of "coordinates" onto space-time, and in general, coordinates don't need to act much like you expect them to.

Anyways, in nice, weak cases (such as looking at Earth's gravitational field), one can get an (extremely good) approximation by imposing coordinates that act similarly to the way coordinates are "supposed" to act. When you do that, one can then define time dilation, and see that it factors into two pieces, one that depends on gravitational potential energy (e.g. this is what is typically thought as "gravitational time dilation"), and one that depends on relative velocity (the stuff from SR).

In any case, in this coordinate system, coordinate time never runs backwards for anything. :tongue:

4. Energy doesn't have mass.

You're probably thinking of K = 1/2 m v^2 (which doesn't apply to relativistic speeds), or E = m c^2 (which is a formula for converting rest mass to energy, not stating the mass possessed by energy).

3. Nov 26, 2004

### Gamish

Thanks for your help on that. I always said "I just dont see how time is a 4th demention". I now know why it is. I used to think time was the effects of motion through space. thanks again :)