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## time slows down when you approach the speed of light?

 Quote by catia ok, so it wasn't my last question. I may have been taking the "relative to the observer" part a little to lightly. but first thank you dbecker for telling me about that book. Everything is relative, right? If there was a space that is completely empty, no vacuum and no background radiation, just complete nothingness and you place one object in that space. ................................

Here is something to ponder. With just one object in an empty universe it would be impossible to tell if it had linear motion or not. However it would be possible to tell if that lonely object was spinning or not. If you had just 2 objects in our otherwise empty universe it would be impossible to tell which one was stationary and which was moving. However, if one of the objects was spinning, you would be able to tell which one is spinning. For practical purposes assume an object is a large body that holds an observer who has a light source, clocks, rulers, mirrors and a few other bits of lab equipment to make measurements with.

 Quote by kev Here is something to ponder. With just one object in an empty universe it would be impossible to tell if it had linear motion or not. However it would be possible to tell if that lonely object was spinning or not.
That is because anything larger than fundamental subatomic particles are not single particles at all; they are composed of two or more particles, and you're back to comparing theit relative orientation.

But if you did have a single subatomic particle, no you would not be able to tell if it were spinning.

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 Quote by DaveC426913 That is because anything larger than fundamental subatomic particles are not single particles at all; they are composed of two or more particles, and you're back to comparing theit relative orientation. But if you did have a single subatomic particle, no you would not be able to tell if it were spinning.
The point I was trying to make is that there appears to be something fundementally more absolute about rotation compared to linear motion. If the Earth was in an otherwise empty universe , you could launch rockets and carry out all sorts of experiments and measurement of "relative orientation" and still be unable to determine if the Earth had absolute linear motion, yet you could by assuming the simplest possible laws of physics infer that the Earth had absolute rotation relative to the vacuum of space.

 Quote by kev The point I was trying to make is that there appears to be something fundementally more absolute about rotation compared to linear motion. If the Earth was in an otherwise empty universe , you could launch rockets and carry out all sorts of experiments and measurement of "relative orientation" and still be unable to determine if the Earth had absolute linear motion, yet you could by assuming the simplest possible laws of physics infer that the Earth had absolute rotation relative to the vacuum of space.
But that is wrong according to Mach's principle (and so, I think, according to GR, but I'm not sure): in the absence of other objects which creates space-time itself, you couldn't say if that only object is spinning or not.

 Quote by catia thank you Ivy... i think i got a bit too philosophical.
Your question was not philosophical at all. See post n. 21.

 Quote by lightarrow They have already answered you, I only add that if you could accelerate (in a reasonable time) to near the speed of light with respect our planet, let's say to 0.999999999999999999999999995 c, then you would reach the present (visible) limit of the universe and back to earth, in one day of your clock, but 28 billions of years on earth (non considering the universe expansion), if it will still exist! Anyway, your biological life would be exactly one year older, not even a little less.
Sorry, it should be one day of course.

Mentor
 Quote by catia Everything is relative, right?
No, there are quantities that are the same in all inertial reference frames, and they are very important in relativity!

For example: measure the energy E and momentum p of an object. Different observers (moving relative to each other) will get different values of E and P. Nevertheless, they will all calculate the same result for the quantity

$$m = \frac{\sqrt {E^2 - (pc)^2}}{c^2}$$

which we call the invariant mass. It's also known as the "rest mass" of the object.

Another example: various observers measure the position and time of two different events. Event 1 occurs at position $x_1$ and time $t_1$. Event 2 occurs at position $x_2$ and time $t_2$. In general, each observer will measure different values for the x's and t's. Nevertheless, they will all calculate the same result for the quantity

$$s = \sqrt{c^2 (t_2 - t_1)^2 - (x_2 - x_1)^2}$$

which we call the invariant (spacetime) interval between the two events.

 to my own post #16 sorry i forgot to say thanks to lightarrow for post #14 i totally missed that. thanks again everyone... i won't ask anymore questions for now.

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 Quote by lightarrow But that is wrong according to Mach's principle (and so, I think, according to GR, but I'm not sure): in the absence of other objects which creates space-time itself, you couldn't say if that only object is spinning or not.
Although Einstien showed an interest in Mach's ideas when he was formulating GR, ultimately he rejected Mach's principle and that principle is not an inherent part of GR or even in agreement with it. By Mach's principle the accelerations felt by an observer on a spinning body would be equivalent to the acceleration caused by the mass of all the distant stars spinning around the stationary body. The maths does not quite work out in exact agreement with GR (as far as I am aware). One difficulty is that even for quite low rates of rotation of the body, assuming the body was stationary would require the distant stars to have a tangential velocity exceeding the speed of light.

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 Quote by kev Although Einstien showed an interest in Mach's ideas when he was formulating GR, ultimately he rejected Mach's principle and that principle is not an inherent part of GR or even in agreement with it. By Mach's principle the accelerations felt by an observer on a spinning body would be equivalent to the acceleration caused by the mass of all the distant stars spinning around the stationary body. The maths does not quite work out in exact agreement with GR (as far as I am aware). One difficulty is that even for quite low rates of rotation of the body, assuming the body was stationary would require the distant stars to have a tangential velocity exceeding the speed of light.
That last point of course would not matter if the distant stars did not imparting information to the body at a rate exceeding the speed of light.

One modification of GR that does include Mach's Principle is the Brans Dicke theory, which is fully covariant so the inertial information conveyed by the scalar field $\phi$ travels at the speed of light.

A further modification of the Brans Dicke theory is Self Creation Cosmology, which also fully includes Mach's Principle and which also does not violate the "light-speed" restriction on information flow.

Garth

 Quote by kev The point I was trying to make is that there appears to be something fundementally more absolute about rotation compared to linear motion. If the Earth was in an otherwise empty universe , you could launch rockets and carry out all sorts of experiments and measurement of "relative orientation" and still be unable to determine if the Earth had absolute linear motion, yet you could by assuming the simplest possible laws of physics infer that the Earth had absolute rotation relative to the vacuum of space.
You wouldn't be able to tell whether the object is spinning or not unless you were on the outside looking in, but then it would be spinning relative to you. If you were on the object you would be rotating with in such a way that you wouldn't be able to tell. Take earth for an example: you throw a ball "straight" up in the air, it comes "straight" down to you. The main reason we can tell that the earth is spinning is due to the changes in our relationship with our sun and moon. This is a very simple point, it can become very complex if we let it, but nonetheless it means that all motion including, including rotational motion or spin, is relative to an external object.

 Quote by dbecker215 You wouldn't be able to tell whether the object is spinning or not unless you were on the outside looking in [...] The main reason we can tell that the earth is spinning is due to the changes in our relationship with our sun and moon.
That's not true, you have forgot centrifugal force.

 Quote by lightarrow That's not true, you have forgot centrifugal force.
If your frame of reference is a point, then you won't experience angular momentumm which means there's no way to tell you're rotating (or more to the point, you cannot rotate).

If your frame of reference is not a point, then you are talking about a non-zero radius, which means your angular momentum can just as easily be treated as translational movement over short distances.

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 Quote by dbecker215 You wouldn't be able to tell whether the object is spinning or not unless you were on the outside looking in, but then it would be spinning relative to you. If you were on the object you would be rotating with in such a way that you wouldn't be able to tell. Take earth for an example: you throw a ball "straight" up in the air, it comes "straight" down to you. The main reason we can tell that the earth is spinning is due to the changes in our relationship with our sun and moon. This is a very simple point, it can become very complex if we let it, but nonetheless it means that all motion including, including rotational motion or spin, is relative to an external object.
If you used a (very long) tape measure you could detect a bulge at the equator (even the sea bulges) due to centripetal force. If you sent sent two directional radio signals East and West you would find that the West going signal would circumnavigate the Earth faster and return first. You could also transport atomic clocks East and West and find the East going clock loses more time than the West going clock. A gyroscope on your desk would precess every 24 hours. You would observe a similar 24 hour precession in a Foucault pendulum. When you weigh an object at sea level on the equator and then weigh it at sea level at the North pole you would expect a difference due to the difference in radius at those points, but you would find there is very little difference due to centripetal force. If a tunnel was drilled through the centre of the Earth from one point on the equator to another, an object dropped into the tunnel would collide with the East side of the tunnel rather than drop straight through. None of these methods require a sun, moon or stars to detect the spin of the Earth.

 You're right that you would be able to figure out whether it was spinning or not but the thing missing in all this is that your spin is still relative. The spin of the object is relative to the coordinate 0 at the axis of the object. So all the measurements that could possibly be done would conclude that the object was spinning relative to the axis, but none would conclude that the object was spinning in relation to the vacuum of space. You still would not be able to conclude that space itself was not spinning.

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 Quote by DaveC426913 If your frame of reference is a point, then you won't experience angular momentumm which means there's no way to tell you're rotating (or more to the point, you cannot rotate)..
It's true that a point particle cannot rotate. However, if we define a point as something with a radius of less than or equal to the Planck length then no elementry particle is a point. Protons and classical electrons are about 10^20 Planck lengths and quark is about 10^17 Planck lengths.

 Quote by DaveC426913 If your frame of reference is not a point, then you are talking about a non-zero radius, which means your angular momentum can just as easily be treated as translational movement over short distances.
If by translational movement you mean linear movement then that kind of motion cannot be detected and can only be expressed relative to an observer. AS HallsOfIvy pointed out, acceleration is absolute in the sense that it can be detected without reference to another body. Rotational or angular motion of a macro object is a form of acceleration and is absolute. I brought up the subject of rotation as the original poster asked if there was anything that was not relative.

 Quote by DaveC426913 If your frame of reference is a point, then you won't experience angular momentumm which means there's no way to tell you're rotating (or more to the point, you cannot rotate). If your frame of reference is not a point, then you are talking about a non-zero radius, which means your angular momentum can just as easily be treated as translational movement over short distances.
In this way you could say accelerations don't exist at all...