Acceleration curves

Aures · Post by **Aures** » Thu Oct 14, 2010 2:06 am

Marvin, the stuff you quoted is all perfectly consistent with what I wrote. As for acceleration, relativity puts no limit on how much you could accelerate. As per my previous example, you could accelerate to 90% of c in one second. or you could do double that and you would reach 99.45% c in one second (although I am being very loose with my units of time here for simplicity). Also, the special theory does not deal with acceleration, you need the general theory for that (although there are various tricks you can use to include certain accelerations without really going beyond the special theory).

Rush, yeah that is a paradox I ran into in uni. Although the way we put it was a rod that travels into the barn where you close the door behind it. If the rod is too long to fit into the barn but fits due to length contraction what happens? Turns out this is a case of physics idealisations getting in the way. That particular paradox dissolves once you take into account you can't have a rod that transmits information along itself instantaneously (see http://www.phys.unsw.edu.au/einsteinlig ... aradox.htm).

Post by **Marvin** » Thu Oct 14, 2010 4:58 am

Show me a formula that doesn't use acceleration. Even the most basic formula:

m = m (at rest) / sqr(1 - v^2 / c^2)

deals in velocity squared and speed of light squared. So, where's the meat?

Nigel_Strange · Post by **Nigel_Strange** » Thu Oct 14, 2010 5:06 am

I guess what is troubling me is the idea that speed is relative until you get near the speed of light, then it requires a fixed vantage point for some reason.

Did this occur to anyone: that the very thing that you are using to measure the distance of something (i.e. the image of it) consists of light? So, how could an observer moving near the speed of light even SEE an object moving in the opposite direction moving near the speed of light? The light would never reach.

Imagine that you are moving at 50% c. The light leaving the back end of your ship would be moving at 1/2 c, right? The light coming off the front of your ship would be moving at 1.5 c, then, wouldn't it? I am sure I'm oversimplifying it, but how does any thought experiment that includes two ships moving away from one another allow one to even observe the other if their combined speed is more than c?

I would imagine that the SHIP would continue moving faster and faster, but the IMAGE of the ship that is visible from the other POV would slow down, so that these theories of time bending and so on are based on observing the light coming off the object, rather than the object itself, which you would not be able to see.

Does that make sense? Makes sense to a layman.

Post by **Marvin** » Thu Oct 14, 2010 6:35 am

I think it was Aures who suggested you consider the ship as not moving at all. (Then, perhaps you could use the formulas I listed.) After all, nothing is totally standing still anyway ... nothing in the entire universe, that I know of. Therefore, your reference point is always moving at some velocity, relative to the motion of the other object.

And I doubt a physicist thinks in terms of "seeing" another object. Relativity seems too hypothetical for any system of measurement as mundane as sight. 'Though, I too would like to hear an explanation for that one.

Aures · Post by **Aures** » Thu Oct 14, 2010 1:03 pm

Hmm, where to start.

Originally posted by Marvin
Show me a formula that doesn't use acceleration. Even the most basic formula:

m = m (at rest) / sqr(1 - v^2 / c^2)

deals in velocity squared and speed of light squared. So, where's the meat?

You just satisfied your own request. Yes it does deal in velocity and light squared. Can you be more specific about what kind of meat you are looking for and why you think it is missing?

Originally posted by Marvin
I think it was Aures who suggested you consider the ship as not moving at all. (Then, perhaps you could use the formulas I listed.) After all, nothing is totally standing still anyway ... nothing in the entire universe, that I know of. Therefore, your reference point is always moving at some velocity, relative to the motion of the other object.

The ship is not moving at all. The ship is moving at .99999999c. The ship is also moving at every other velocity at the same time it is stationary and moving at nearly the speed of light. There are an infinity of inertial reference frames and all of them are as valid as each other. The ship has a different velocity with respect to each of them.

Every other object in the universe is in exactly the same situation. All is still, all is in motion. Velocity is relative.

Originally posted by Marvin
And I doubt a physicist thinks in terms of "seeing" another object. Relativity seems too hypothetical for any system of measurement as mundane as sight. 'Though, I too would like to hear an explanation for that one.

Actually a lot of relativity is formulated in exactly this way, by measuring light from another object. According to Einstein it was a major part of his thinking when developing the theories and it shows in his work.

Originally posted by Nigel_Strange
I guess what is troubling me is the idea that speed is relative until you get near the speed of light, then it requires a fixed vantage point for some reason.

Not true, see my point about relative motion. Nothing that is below the speed of light is any closer to the speed of light than anything else. The rules are different at the speed of light, but "near the speed of light" is a subjective concept. You are just as near the speed of light as the fastest proton in the LHC. You are just not moving fast with respect to the Earth while the proton is.

Originally posted by Nigel_Strange
Does that make sense? Makes sense to a layman.

Sorry, not really. At least in the context of relativity in open space. But it is ok, I knew I would have to go into more depth about the relative motion of photons. Here is a little thought experiment to help you see why it is not right to talk about two photons going in the opposite direction as travelling at 2c relative to each other.

Imagine that instead of firing the photons off in opposite directions we fire them at 60 degrees to each other. The two paths the light takes plus the line joining pulses then form three sides of an equilateral triangle. Therefore, you may want to say the pulses are moving apart from each other at exactly the speed of light.

But, now consider what happens if we add another observer. This observer is moving at .866c (the exact value is 0.5*(3^0.5)c) and passes us at the same time as we fire off the light pulses. What does this observer see? He is moving at just the right speed to stay on the line joining the light pulses. As far as this observer is concerned, the light is moving directly away from him. It is moving directly away from him at the speed of light. Our observer is none other than the observer from the thought experiment in a previous post who calculated the light was moving apart at 2c.

We can now consider him to have emitted the light pulses in opposite directions as per the previous experiment and the other observer to be moving at the velocity required to see the light moving at an angle of 60 degrees. Neither viewpoint is more valid than the other. So which is it? Are they moving apart at c or 2c? Neither, because it does not make sense to ascribe relative velocities to the photons in that way.

Nigel_Strange, I'm afraid you are thinking of something that works more like the sound barrier than the speed of light. There is some absolute aether in your thinking that dictates what is close to the speed of light and what isn't. That kind of aether does not exist (EDIT: at least in the theory of relativity), ask Marvin's textbook. Although, you were not all that far off some situations you can get when light is travelling in a medium rather than in empty space (see Cherenkov Radiation to get you started).

[Edited on 14-10-2010 by Aures]

Post by **Marvin** » Thu Oct 14, 2010 3:19 pm

Originally posted by Aures
Originally posted by Marvin
Show me a formula that doesn't use acceleration. Even the most basic formula:

m = m (at rest) / sqr(1 - v^2 / c^2)

deals in velocity squared and speed of light squared. So, where's the meat?
You just satisfied your own request. Yes it does deal in velocity and light squared. Can you be more specific about what kind of meat you are looking for and why you think it is missing?

That formula (and all others that I can think of) does not deal with velocity ... it deals with velocity squared.

v^2 = acceleration

Where can you show me a formula that states velocity (un-squared) cannot exceed 186,000 mi/sec in this universe?

Aures · Post by **Aures** » Thu Oct 14, 2010 4:11 pm

Umm, the derivative of velocity is acceleration (in various notations dv/dt, v', d^2x/dt^2, x'', a etc). Velocity squared is velocity squared and is a different entity. Yoda moment I believe.

Post by **Marvin** » Thu Oct 14, 2010 4:34 pm

So, 186,000 miles per second per second is not acceleration. That's too bad.

Aures · Post by **Aures** » Thu Oct 14, 2010 11:16 pm

186,000 miles per second per second is a very fast acceleration. It is what defines the event horizon of a black hole. 186,000 miles per second is the speed of light.

Post by **Marvin** » Fri Oct 15, 2010 12:21 am

How fast can light go in circles 'cause I get the feeling that's about what we're doing here?

Aures · Post by **Aures** » Fri Oct 15, 2010 3:22 am

Agreed (btw, 186,000 miles per second).

I'll just take it as another reason why it would be good to make small adjustments to make the game more accurately reflect relativity. What is left of my suggestion boils down to pretty much an aesthetic change so I will leave it be until the real issues have been sorted.

Post by **Marvin** » Fri Oct 15, 2010 4:25 am

Originally posted by Aures

...I will leave it be until the real issues have been sorted.

Very sensible idea.

soulsacrifice · Post by **soulsacrifice** » Fri Oct 15, 2010 3:02 pm

Originally posted by Aures
Agreed (btw, 186,000 miles per second).

Surely for light to travel in circles it would have to travel through a medium of some sort (glass) and therefore unable to travel at it's maximum speed?

Post by **Marvin** » Fri Oct 15, 2010 11:33 pm

Gravity can bend light. But what are the parameters to keep light in orbit, continually going in circles?

Trent · Post by **Trent** » Sun Oct 17, 2010 5:26 am

OK Relative to our observation on Earth, a galaxy is moving directly away from us at exactly the speed of light. Would we be able to detect the galaxy? It seems (to me) that the light leaving that galaxy would be perfectly at rest - relative to Earth - and thus never move any closer to Earth.

Second question - what if our Galaxy the Milky Way, having been propelled away from the center of the universe by the Big Bang, is moving one direction at 1/2 the speed of light from the center of the universe, and a galaxy on the other side of the universe is moving directly opposite at half the speed of light. Will light from either galaxy ever reach the other galaxy?

Third question - two galaxies are moving away from the center of the universe, at angles to one another. Do we have to factor in the speed of both universes relative to the center of the universe to accurately calculate how long it took the light to arrive at Earth (and hence, how distant the galaxy is from us?) Reason I ask this is it would seem that in order to calculate how distant any other galaxy is away from ours, you would need to know the relative speed of each from another fixed body. In effect, we're running in to light sent to us at a tangent - assuming that at any point in time light emitted from one galaxy cannot travel a straight line to the other, but rather, we're running in to light emitted at an "angle" relative to us.