Questions about Special Relativity

[swansont]

Why can't v be greater than c?

 

Because the answer would be unphysical. What would an imaginary length or time mean?

[swansont]

Prove this.

 

I expect to see the time dilation formula utilized.

 

After time t has passed on one clock, time t' will have passed on the other, where t and t' are given by the time dilation formula.

 

Instead of a fat clock and a skinny clock, let's make them identical. Is there any way of telling them apart, under the circumstance of this test, if you were an observer moving with a clock?

[5614]

If they were totaly identical including speed, time they showed etc you couldn't tell them apart.

 

If they were identically built but ran [as in showing time, not sprinting down 100m!] independant of each other and were moving at different speeds then the time shown on each would be different.

[swansont]

If they were totaly identical including speed' date=' time they showed etc you couldn't tell them apart.

 

If they were identically built but ran [as in showing time, not sprinting down 100m!'] independant of each other and were moving at different speeds then the time shown on each would be different.

 

But they can only be running a different speeds to a third observer. To each other, the speeds must be the same.

[5614]

But they can only be running a different speeds to a third observer. To each other, the speeds must be the same.

Are you making the assumption that a clock cannot read itself?

(Which I suppose is a fair assumption!)

[Johnny5]

Because a clock must have mass therefore cannot exceed the speed of light.

 

As we're dealing with SR which is part of physics lets just agree with the laws of physics' date=' ie. nothing with mass can go FTL or c.[/quote']

 

So you are already assuming that the formula is correct? Then you should derive it.

[Johnny5]

Because the answer would be unphysical. What would an imaginary length or time mean?

 

They would mean nothing that I have ever pondered.

 

Let me state my position.

 

Time is measured by clocks.

Length is measured by rulers.

 

With that in mind, imaginary time is meaningless.

With that in mind, imaginary length is meaningless.

[Johnny5]

After time t has passed on one clock' date=' time t' will have passed on the other, where t and t' are given by the time dilation formula.

[/quote']

 

The time dilation formula has not been proven by either you or 5614, here and now.

[Johnny5]

 

Instead of a fat clock and a skinny clock' date=' let's make them identical. Is there any way of telling them apart, under the circumstance of this test, if you were an observer moving with a clock?[/quote']

 

The clocks are supposed to be identical.

 

They are both in inertial reference frames, and neither of them has any force exerted on them, and their relative speed was v.

 

One way to tell them apart, is by their location in the universe.

 

They are identical, in the following sense: they each have the same rest rate.

 

In other words, if they are at rest relative to one another, and they are in sync at one moment in time, then they remain in sync.

[5614]

So you are already assuming that the formula is correct? Then you should derive it........[different post]........ The time dilation formula has not been proven by either you [swansont] [/i']or 5614, here and now.

If we assume that the formula is correct we do not need to derive it. Only if you doubt it's correctness must you derive it to prove it for/to yourself.

 

At the same time I did give you a link when I first wrote (or a got an image of) the time dilation formula.... and I wouldn't know how to derive it myself anyway.

[Johnny5]

If they were identically built but ran [as in showing time' date= not sprinting down 100m!] independant of each other and were moving at different speeds then the time shown on each would be different.

 

How did you arrive at the conclusion that the time shown on each would be different?

[Johnny5]

But they can only be running a different speeds to a third observer. To each other, the speeds must be the same.

 

Yes.

 

In either frame, when they compute the speed of the other using rulers and clocks at rest, they must come up with the same relative speed v.

[swansont]

Are you making the assumption that a clock cannot read itself?

(Which I suppose is a fair assumption!)

 

I assume an observer with the clock is doing the reading. Any reference to what one clock "sees" is referring to any observer with the clock.

[swansont]

The time dilation formula has not been proven by either you or 5614, here and now.

 

And neither of us have reinvented the wheel, either. If you need to see the derivation, there are libraries and the great big world wide web at your disposal.

[5614]

How did you arrive at the conclusion that the time shown on each would be different?

It was a play on the word "identical" because if they were totaly identical then even if time dilation was correct and they moved at different speeds to be identical they must both still show the same time.

 

Time dilation says that as one clock moves relative to another time will slow down for the moving clock.

 

Incidentally look here:

http://en.wikipedia.org/wiki/Time_dilation

and look at the:

"speed vs length due to length contraction vs "relativistic mass" vs time due to time dilation"

table, it's quite interesting.

[swansont]

They would mean nothing that I have ever pondered.

 

Let me state my position.

 

Time is measured by clocks.

Length is measured by rulers.

 

With that in mind' date=' imaginary time is meaningless.

With that in mind, imaginary length is meaningless.[/quote']

 

Good. So if a valid formula gives an unphysical answer for some values of a variable, those values are not physically attainable.

[swansont]

The clocks are supposed to be identical.

 

They are both in inertial reference frames' date=' and neither of them has any force exerted on them, and their relative speed was v.

 

One way to tell them apart, is by their location in the universe.

 

They are identical, in the following sense: they each have the same rest rate.

 

In other words, if they are at rest relative to one another, and they are in sync at one moment in time, then they remain in sync.[/quote']

 

But there is nothing else in the universe to establish their position. So they are indistinguishable. So one observer can't see something different than the other observer.

[5614]

But they can only be running a different speeds to a third observer. To each other, the speeds must be the same..... [different post']........ I assume an observer with the clock is doing the reading. Any reference to what one clock "sees" is referring to any observer with the clock.

A and B are moving relative to each other.

 

A and B are both a clock/clock-reader pair.

 

Due to time dilation either A's clock or B's clock will be running faster (or slower) than the other one?

 

So why can only C (our third observer) notice the difference between them?

 

Surely if B is running faster then it can see that A is running slower?

[swansont]

It was a play on the word "identical" because if they were totaly identical then even if time dilation was correct and they moved at different speeds to be identical they must both still show the same time.

 

Time dilation says that as one clock moves relative to another time will slow down for the moving clock.

 

There can be no "different speeds" though. There is only one speed variable, v, and they both measure it to be the same value.

[Johnny5]

 

Time dilation says that as one clock moves relative to another time will slow down for the moving clock.

 

And this is what I am saying leads to a contradiction. Interesting article by the way, I thought it was very well written. Wikipedia seems to be getting better.

[Johnny5]

But there is nothing else in the universe to establish their position. So they are indistinguishable. So one observer can't see something different than the other observer.

 

I'm not sure what you mean by "indistinguishable" here.

 

We can establish their position as follows:

 

There is one and only one place in the universe, which is the center of mass of the universe. Let a three dimensional inertial reference frame have been set up there, with its origin permanently being the center of inertia of the universe.

 

So we can use the center of mass of the universe to establish their position.

 

The universe might not be homogenous.

 

I understand the time dilation formula, I really wish you would attempt to derive it.

[5614]

There can be no "different speeds" though. There is only one speed variable, v, and they both measure it to be the same value.

Why not?

 

A and B are the only things in the universe.

 

Lets make a virtual frame just for this example... relative to this virtual frame which is about to disapear A is moving at 10mph and B at 20mph.... virtual frame just died... A and B still retain that speed.

 

So to A it looks like B is going at 10mph

And to B is looks like A is going at 10mph

 

There's a speed difference in that one is moving relative to the other.

 

Therefore isn't one of the clocks going to be going slower?

[Johnny5]

Why not?

 

A and B are the only things in the universe.

 

Lets make a virtual frame just for this example... relative to this virtual frame which is about to disapear A is moving at 10mph and B at 20mph.... virtual frame just died... A and B still retain that speed.

 

So to A it looks like B is going at 10mph

And to B is looks like A is going at 10mph

 

There's a speed difference in that one is moving relative to the other.

 

Therefore isn't one of the clocks going to be going slower?

 

There is such a high degree of symmetry in the problem you should expect the clocks to tick at the same rate. You are not exploiting that fact that each clock is in an inertial frame. I believe I added that neither is being subjected to any external force.

 

and I don't know what you meant by a virtual frame.

 

 

In A's rest frame, the relative speed is v1.

In B's rest frame, the relative speed is v2.

 

As long as they use the same units of length, and time, and the same definition of relative speed, it must be the case that:

 

v1=v2.

 

 

Actually, that fact has nothing whatsoever to do with measurements. It's a fact independently of how they measure v, or even if they can measure v.

 

It's just that if they use the same units, their computations will yield the same answer.

[5614]

OK, virtual frame was there just go give frame A and B a speed to compare to... forget it, read this instead:

 

A knows B is moving

B knows A is moving

They are both inteligent and know that without a 3rd frame they both could be moving but there is no 3rd frame, they know that either one or both are moving.

 

There is (I know they're not accelerating, but at a constant speed) a speed difference in that one is travelling faster than the other.

 

Because one is moving faster surely their clock is moving slower?

 

---

 

Deriving time dilation formula:

http://www.google.co.uk/search?hl=en&q=derive+time+dilation+formula&meta=

(google is your friend!)

[Johnny5]

OK' date=' virtual frame was there just go give frame A and B a speed to compare to... forget it, read this instead:

 

A knows B is moving

B knows A is moving

They are both inteligent and know that without a 3rd frame they both could be moving but there is no 3rd frame, they know that either one or both are moving.

 

There is (I know they're not accelerating, but at a constant speed) a speed difference in that one is travelling faster than the other.

 

Because one is moving faster surely their clock is moving slower?

 

--- [/quote']

 

I am not following you.

 

You have treated motion as absolute. Did you mean to do that?

 

I would have said...

 

A knows B is moving relative to A.

B knows A is moving relative to B.

 

It doesn't make sense to say that one of them could be absolutely at rest. Rest only makes sense after you choose a frame to define speed in.

 

Also...

 

 

Deriving time dilation formula:

http://www.google.co.uk/search?hl=en&q=derive+time+dilation+formula&meta=

(google is your friend!)

 

Are you familiar with the light clock derivation of the time dilation formula?