Is Relativity Reality?

[Twiglet]

A simple yes or no would do.

You can put numbers into the equation. When you do then you obtain a negative length and time going backwards
If you try to calculate the energy required to accelerate matter to the speed of light, the answer is infinite at v=c.

That is why your question doesn't apply to a real problem, as experimentally, within relativity, particles neither possess infinite energy or go backwards in time (well, actually, technically they sort of can, but not for very long, and the effect is not in relativity but I digress).

[Farsight]

Farsight and Mistermack:

Please answer the following basic question using special relativity.

Two objects, each one metre long, are moving away from each other with a speed of 2.7x10^8m/s

How long does object B appear as observed from object A?

That's .9c, so using applying the Lorentz factor √(1-v²/c²) and natural units where c=1:

length = √(1-.9²/1²)

length = √(1-.81)

length = √(.19)

length = .435 metres

Next, assume Object A is at rest, and object B is moving away from it at 2.7x10^8m/s
Object B carries a clock and waits for 1 second to elapse.
How long has elapsed on Object As clock.

Assume c=3x10^8m/s
Please show working.

Thankyou.

I presume you're asking what B would observe if he could see A's clock, and that you aware that the situation is symmetrical. The working is as above, but we're dealing with time dilation rather than length contraction, so take a reciprocal. The answer is 1/.435 seconds or:

2.3 seconds.

Note that arithmetical exercises doesn't get to the bottom of why we observe length contractiobn and time dilation, or indeed why c is the limit. For this you have to understand the underlying Pythagoras' Theorem and E=mc². And to understand the latter you have to understand the terms. You have to understand E, m, and c, which means you have to understand energy mass and time. Only then do you fully understand special relativity.

Edit:

The distinction is basic. Relativity makes assumptions.

Only then do you get past the assumptions and get to the bottom of it. Then you appreciate that mistermack, in a roundabout way, is right.

[ChildInAZoo]

A simple yes or no would do.

Sure, if you we not interested in anything about SR.

[Twiglet]

Farsight and Mistermack:

Please answer the following basic question using special relativity.

Two objects, each one metre long, are moving away from each other with a speed of 2.7x10^8m/s

How long does object B appear as observed from object A?

That's .9c, so using applying the Lorentz factor √(1-v²/c²) and natural units where c=1:

length = √(1-.9²/1²)

length = √(1-.81)

length = √(.19)

length = .435 metres

Next, assume Object A is at rest, and object B is moving away from it at 2.7x10^8m/s
Object B carries a clock and waits for 1 second to elapse.
How long has elapsed on Object As clock.

Assume c=3x10^8m/s
Please show working.

Thankyou.

I presume you're asking what B would observe if he could see A's clock, and that you aware that the situation is symmetrical. The working is as above, but we're dealing with time dilation rather than length contraction, so take a reciprocal. The answer is 1/.435 seconds or:

2.3 seconds.

Note that arithmetical exercises doesn't get to the bottom of why we observe length contractiobn and time dilation, or indeed why c is the limit. For this you have to understand the underlying Pythagoras' Theorem and E=mc². And to understand the latter you have to understand the terms. You have to understand E, m, and c, which means you have to understand energy mass and time. Only then do you fully understand special relativity.

Edit:

The distinction is basic. Relativity makes assumptions.

Only then do you get past the assumptions and get to the bottom of it. Then you appreciate that mistermack, in a roundabout way, is right.

Alright farsight, you obtained the correct numerical answers.

How about supplying the less trivial solution which speaks to the heart of mistermacks conceptual query.

Consider and observer at rest. A particle moves in direction x at 2.7x10^8 m/s. The other moves in direction -x at 2.7x10^8m/s. Taking the frame of reference of either particle, calculate the speed of the other.

That is a less trivial problem. It requires no trigonometry to calculate the answer.

[mistermack]

You can put numbers into the equation. When you do then you obtain a negative length and time going backwards
If you try to calculate the energy required to accelerate matter to the speed of light, the answer is infinite at v=c.

Jeez, it's like pulling teeth from a statue. However, I believe enmeshed in there somewhere is some kind of affirmative.
So the range of valid frames IS reduced from infinity to a finite range by the limit of c. So my ''little sphere'' of valid frames is correct in the case of a single particle.
I have a feeling Einstein would have just given me a straight yes.
.

[ChildInAZoo]

You can put numbers into the equation. When you do then you obtain a negative length and time going backwards
If you try to calculate the energy required to accelerate matter to the speed of light, the answer is infinite at v=c.

Jeez, it's like pulling teeth from a statue. However, I believe enmeshed in there somewhere is some kind of affirmative.
So the range of valid frames IS reduced from infinity to a finite range by the limit of c. So my ''little sphere'' of valid frames is correct in the case of a single particle.
I have a feeling Einstein would have just given me a straight yes.
.

Why don't you read what Einstein actually wrote about special relativity and find out?

If you do, you will find that we can use an infinite amount of reference frames to describe pretty much any situation, as long as the frames are moving in uniform translatory motion to each other. (The only exceptions are those cases where there is a significant amount of gravity involved.) Once you have a legitimate description in one frame, one can translate into any frame and one will discover that there is nothing in that frame moving at a speed greater than c.

[mistermack]

Blimey childinazoo, you've managed to completely miss the point, in spite of me practically spelling it out letter by letter. Or are you pulling my leg?
At least Twiglet got the point, even if it was painful trying to get a grudging concession that there is NOT an infinite choice of frames in a world limited by c.
.

[ChildInAZoo]

Blimey childinazoo, you've managed to completely miss the point, in spite of me practically spelling it out letter by letter. Or are you pulling my leg?

Maybe you should restate your point. Regardless, your argument hasn't anything to do with the actual theory with the proper name "Special Relativity".

At least Twiglet got the point, even if it was painful trying to get a grudging concession that there is NOT an infinite choice of frames in a world limited by c.

That's not what he said. At no point did he limit the available frames to a finite number. Again, you find this hard to understand because you decided to criticize SR before you bothered to learn SR.

[mistermack]

Maybe you should restate your point.

I honestly couldn't make it any clearer. It's there, in the simplest language I can muster. I claimed that the RANGE of valid frames is reduced from infinity by the real-life limit of c. Nobody is talking about the NUMBER of valid frames at this point, just the RANGE.
Is it or is it not valid to choose a frame such that a particle would be moving at over c?

That's not what he said. At no point did he limit the available frames to a finite number.

Finite RANGE!! I suggested attempting a Lorenz transformation for a frame receding at over c, 350,000 kps. Twiglet commented ''You can put numbers into the equation. When you do then you obtain a negative length and time going backwards
If you try to calculate the energy required to accelerate matter to the speed of light, the answer is infinite at v=c.''
I take that to mean that that frame is invalid. I'm sure twiglet will correct me if he mean't something else.
Anyway, as far as I can see, I'm only asking people to state the bleedin obvious.
(or refute it)
.

[mistermack]

Just to prove that I have the patience of a saint, here we go again.
The Universe consists of one single particle in otherwise empty space.
The diagram below shows what I think is the maximum range of valid reference frames in the blue shaded volume of the sphere. Is that right, or can you choose a frame who's velocity relative to the particle is greater than 300,000 kps? ie, that falls outside the blue volume?

[ChildInAZoo]

I honestly couldn't make it any clearer. It's there, in the simplest language I can muster. I claimed that the RANGE of valid frames is reduced from infinity by the real-life limit of c. Nobody is talking about the NUMBER of valid frames at this point, just the RANGE.
Is it or is it not valid to choose a frame such that a particle would be moving at over c?

Technically, if one wants to produce a situation where one can produce meaningful physical results, one cannot produce a reference frame where a particle is moving faster than c (as measured against the coordinates). This still leaves a set of reference frames of denumerable cardinality.

[ChildInAZoo]

Just to prove that I have the patience of a saint, here we go again.
The Universe consists of one single particle in otherwise empty space.
The diagram below shows what I think is the maximum range of valid reference frames in the blue shaded volume of the sphere. Is that right, or can you choose a frame who's velocity relative to the particle is greater than 300,000 kps? ie, that falls outside the blue volume?

You can't chose a meaningful reference frame in which the velocity of the particle is greater than the speed of light, but this doesn't have anything to do with the blue circle. That image is of a specific reference frame and one cannot encapsulate another reference frame within it.

[mistermack]

I give up. You're taking the mick.

[newolder]

Just to prove that I have the patience of a saint, here we go again.
The Universe consists of one single particle in otherwise empty space.
The diagram below shows what I think is the maximum range of valid reference frames in the blue shaded volume of the sphere. Is that right, or can you choose a frame who's velocity relative to the particle is greater than 300,000 kps? ie, that falls outside the blue volume?

This is simpler:

Source
The scope of a light cone is infinite, the scope of tachyons (B) is infinitely larger and there is no largest infinity (Cantor).

[mistermack]

Newolder, if you're saying that particles exceeding c produces complete gibberish, then I agree completely. And people have said on this thread many times, no particle can move at c.
But try to get people to agree to the bleedin obvious consequence of that, that you can't choose a frame in which a particle would be moving at more than c, and people change the subject fast. I can't see what is so scary about the obvious.

Childinazoo nearly got there :

Technically, if one wants to produce a situation where one can produce meaningful physical results, one cannot produce a reference frame where a particle is moving faster than c (as measured against the coordinates).

But then he fudged it :

This still leaves a set of reference frames of denumerable cardinality.

.