Relativity Made Simple

[Pmb]

A-wal: You really need to stop being as rude as you are. Your rudeness is rooted in the amount of arrogance that you've been displaying here. You've shown that anytime someone has pointed out an error that you've made, like I did, all you've been able to do is claim it was in fact their error and it was they who had a misconception. While it's quite clear to me that the rest of the forum knows this all to well it might be worth pointing it out to you one last time so that I may at least see if you're able to admit your mistakes. The following example demonstrates the mistake you made which you claimed was my misconception. I explained the following (the only mistake I made was writing "he" instead of "the" which I correct here)

 

 

E.g. a car can travel at 55 mph relative to the road. If a man is standing on the side of the road and one car is moving at 55 mph in the +x direction and the other at 55 mph in the -x direction then there is nothing moving at 110 mph. The only thing having to do with 110 mph is the distance between the two objects is changing at a rate of 110 mph.

There was nothing in this statement that referred to any other frame of reference other than the car's frame of reference. To think it did meant that you weren't paying attention to the subject matter or the point being made.

 

Therefore when you started saying "You can use either car or the road as a frame of reference .... there's two objects moving away from each other at 110 mph...." when that had absolutely nothing to do with my post or the subject I was talking about.

 

I was clearly referring to Philip1182's post where he said

 

... the oncoming light beam is traveling twice the speed of light.

which was a misunderstanding on his part since there is ---->>>> not one single frame <<<<---- in which light itself is traveling at something other than c. So I gave him an example which demonstrates that a car moving relative to a road at 55 mph is only moving at 555 mph relative to the road even though the rate of change of the distance between the two cars is changing at 110 mph.

 

So not only did you miss the entire point that I made, and you were the only person to miss the point you found the need to be quite rude to do it and you remain quite rude even with the warnings you got. Let's see how long you maintain that attitude when I report each post you make with you being rude. Stop being rude and act more polite like the other members here are.

 

My comment was in regards to post #2 where

 

 

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[phillip1882]

i guess i'm not able to wrap my head around the fact the different obsevers experance different time dilation and space dilation.

 

in the example i gave of  two objects traveling at 60% of light, one of the two stationary objects, A or D should see their combined speed as 1.2c correct? if so, this suggests to me that light is not the maximum possible speed, because the reative velocity between two objects form another perspective can be higher than c.

 

and i still say your misinterpeting einstien's idea. light does not infinitely dilate time and we can prove that by the fact that it doesn't travel instentaneously. don't try to word twist out of this, you cannot both claim light having a non instintaneous velocity and an instintaneous one any more than i can claim 2+2 = 4 and not 4.

Edited June 30, 2015 by phillip1882

[CraigD]

for example imagine one object traveling away form the earth toward the moon at 60% the speed of light realitive to the earth, and another object traveling away from the moon tward the earth at 60% of the speed of light relative to the moon. what would the speed of the two objects be toward each other?

Your question, Phillip, can be answered with a simple algebraic transformation of the “how to add velocities under Special Relativity” question A-Wal asked a bit later, and I answered in this post.

 

Start with

[math]v_{ca} = \frac{v_{ba} + v_{cb}}{1 + v_{ba} v_{cb}}[/math]

Where: [math]v_{ca}[/math] is the velocity of a body [math]C[/math] relative to a body [math]A[/math],

[math]v_{ba}[/math] is the velocity of a body [math]B[/math] relative to [math]A[/math],

[math]v_{cb}[/math] is the velocity of [math]C[/math] relative [math]B[/math],

and all velocities are in units of the speed of light, c.

 

You can sketch these bodies and velocities like this:

[math]A \,\, {B\overrightarrow{\,v_{ba}}} \,\,{C\overrightarrow{\,v_{ca}}} [/math]

[math]{\overleftarrow{-v_{ba}\,}A} \,\, B \,\, {C\overrightarrow{\,v_{cb}}} [/math]

 

What you want to calculate, though, isn’t [math]v_{ca}[/math], but [math]v_{cb}[/math]. A little algebra gives

[math]v_{cb} = \frac{v_{ca} - v_{ba}}{1 - v_{ca} v_{ba}}[/math]

 

which you can sketch like this:

[math]A \,\, {B\overrightarrow{\,v_{ba}}} \,\,{\overleftarrow{-v_{ca}\,}C} [/math]

[math]{A\overrightarrow{\,-v_{ca}}} \,\, {B\overrightarrow{\,-v_{cb}}} \,\, C [/math]

 

[math]A[/math] is the earth, [math]B[/math] is the object traveling away from Earth toward the Moon, and [math]C[/math] is the object traveling toward the Earth from the Moon. You don’t need to a separate term for the Moon, since it’s at rest relative to the Earth.

 

Given [math]V_{ba}[/math]= 0.6 c, [math]V_{ca}[/math]= -0.6 c,

[math]v_{cb} = \frac{-0.6 - 0.6}{1 – (-0.6 \cdot 0.6} \,=\, \frac{15}{17} \,\mbox{c} \,=\, 0.\overline{8823529411764705} \,\mbox{c}[/math]

 

and i still say your misinterpeting einstien's idea. light does not infinitely dilate time and we can prove that by the fact that it doesn't travel instentaneously.

I think you’re referring to a statement like

From the perspective of a photon that's travelling at the speed of light, time and space are infinitely time dilated and length contracted. Nothing with mass can ever experience this frame of reference.

A-wal’s correctly describing a consequence of special relativity, though, because, as he notes, nothing with mass (like a human being of a clock) can experience it, it’s entirely a thought exercise. A math purist would say “from the perspective of a body approaching the speed of light, time and space approach dilation and length contraction”, but if you can forgive slightly sloppy math, what it’s saying is simply that the “Lorentz term” that give time dilation and length contraction, [math]\sqrt{1 -\left(\frac{v}{c}\right)^2 }[/math] is 0 when [math]v=c[/math].

 

So, from the perspective of a photon, the universe in its direction of travel is “infinitely length contracted” to a length of zero. From the perspective of any observer of the photon, if somehow the photon had a clock, it would be “infinitely time dilated” so that it showed no change in time. No observer can share the inertial frame of photon, nor can photons have clocks, so this is an exercise in imagination – an accurate one, but of observations that can never actually be made.

[A-wal]

It's [math]v_{ca} = \frac{v_{ba} + v_{cb}}{1 + v_{ba} v_{cb}}[/math]

Where: [math]v_{ca}[/math] is the velocity of a body [math]C[/math] relative to a body [math]A[/math],

[math]v_{ba}[/math] is the velocity of a body [math]B[/math] relative to [math]A[/math],

[math]v_{cb}[/math] is the velocity of [math]C[/math] relative [math]B[/math],

and all velocities are in units of the speed of light, c.

 

For example, if A sees B moving at 0.75 c, and B sees C moving in the same direction at 0.75 c, A sees C moving at [math]v_{ca} = \frac{0.75 + 0.75}{1 + 0.75 \cdot 0.75} = 0.96[/math] c

 

(notice I didn’t use your example’s 0.6 c, because that gives [math]v_{ca} = \frac{15}{17}[/math] c, which is confusing to write as a decimal numeral, because its digits repeat infinitely. When writing examples, it’s helpful to pick your values to give easy-to-read results)

 

Notice [math]v_{cb}[/math] is 1, [math]v_{ca}[/math] will be 1 regardless of [math]v_{ba}[/math], which is just another way of saying that the speed of a body seen traveling the speed of light by observer must also been seen traveling the speed of light by any other observer.

Ah, thankyou. So v = ( a + b ) / ( 1 + ( ab ) ), so .5c +.5c = exactly .8c. That's very handy. Now I need to see if the relativity wheel thing works by getting the amount of time dilation/length contraction it predicts and then squaring it to get the difference in relative velocities between a liniar progression and the real one. I'm sure it does work but I should check.

 

A-wal: You really need to stop being as rude as you are. Your rudeness is rooted in the amount of arrogance that you've been displaying here. You've shown that anytime someone has pointed out an error that you've made, like I did, all you've been able to do is claim it was in fact their error and it was they who had a misconception.

Because you haven't pointed out any errors, you've simply highlighted your inability to follow basic English. You're the one being rude, not me. I haven't been rude yet, but I can if you'd like me to be.

 

While it's quite clear to me that the rest of the forum knows this all to well it might be worth pointing it out to you one last time so that I may at least see if you're able to admit your mistakes. The following example demonstrates the mistake you made which you claimed was my misconception.

Yea that's it, try to convince anyone reading that everybody else has the opinion you want them to have in the hope that they'll follow along with what you've attempted to frabricate. :)

 

There was nothing in this statement that referred to any other frame of reference other than the car's frame of reference. To think it did meant that you weren't paying attention to the subject matter or the point being made.

 

Therefore when you started saying "You can use either car or the road as a frame of reference .... there's two objects moving away from each other at 110 mph...." when that had absolutely nothing to do with my post or the subject I was talking about.

This statement is false:

If a man is standing on he side of the road and one car is moving at 55mph in the +x direction and the other at 55mph in the -x direction then there is nothing moving at 110 mph.

Yes there is. The two objects are moving at 110mph relative to each other with respect to the road. You should have said 'there is no object moving at 110mph relative to another object in their own frame of reference.' You didn't say that, therefore it's your error, not mine. Deal with it.

 

So not only did you miss the entire point that I made, and you were the only person to miss the point you found the need to be quite rude to do it and you remain quite rude even with the warnings you got. Let's see how long you maintain that attitude when I report each post you make with you being rude. Stop being rude and act more polite like the other members here are.

You mean when you :cry: to an admin. You're one of those. Why does that not supprise me?

 

I know what I'm talking about since I've been a relativist for over two decades and I run into ignorant people such as yourself on a daily basis posting nonsense like this. And I've been trained by some of the best relativists and physicists that there are.

:LOL:

Also the four dimensions are not at right angles to each other. That's not a physically meaningful statement. The only thing that can be at right angles are spatial axes.

What you lack the understanding of is that it only applies to the equations of physics and not to physical reality. It's only treated as being equivalent mathematically. Every expert in relativity knows this and I know some of the best experts.

If a man is standing on he side of the road and one car is moving at 55mph in the +x direction and the other at 55mph in the -x direction then there is nothing moving at 110 mph.

I hope you're not lying. It's funnier if it's true.

 

i guess i'm not able to wrap my head around the fact the different obsevers experance different time dilation and space dilation.

Keep it simple. The speed of light is the same relative to every inertial observer, so the amount of time dilation and length contraction experienced by inertial observers that are in motion relative to each other has to vary in different frames of reference to keep the speed of light the same in every inertial frame.

 

More in depth:

Object A is moving away from Earth at half the speed of light. Object B is moving in the same direction and away from object A at half the speed of light. Object B is moving away from Earth at 0.8 light speed. To understand why it's 0.8, Earth shines a beam of light that passes object A at the speed of light from the perspective of object A, but at half the speed of light from the perspective of object B. The light then passes object B at the speed of light from the perspective of object B, but at half the speed of light from the perspective of object A. The situation is symetric with regards to object A and object B, both see the other as time dilated and length contracted so that the speed of light is the same from both frames of reference, but the situation isn't symetric from the perspective of Earth. From Earth's frame of reference the light passes object A at 0.5 light speed and passes object B at 0.2 light speed. If object B shines a light towards Earth object B sees it move past Earth at 0.2 light speed, the situation with regards to object B and Earth is symetric, just like the situation between object A and object B, except the relative velocity is greater (0.8 light speed). For object A to stay exacrtly half way between Earth and object B it has to be moving at 0.5 light speed relative to both of them rather than 0.4 light speed because it's undergoing less time dilation and length contraction from the perspective of Earth and object B. This is how it has to work to keep the speed of light the same for all three inertial observers.

 

in the example i gave of  two objects traveling at 60% of light, one of the two stationary objects, A or D should see their combined speed as 1.2c correct? if so, this suggests to me that light is not the maximum possible speed, because the reative velocity between two objects form another perspective can be higher than c.

"one of the two stationary objects" There's no such thing. An object can only be said to be stationary relative to another object.

 

Yes, if an object is moving away from you at half the speed of light and another object is moving away from in the opposite direction at half the speed of light then from your perspective the two objects are moving away from each other at the full speed of light, but at 0.8 light speed from their own perspectives. In this sense the maximum possible speed is anything under twice the speed of light, but this needs a third observer. No object can move at or greater than the speed of light relative to any other object.

 

and i still say your misinterpeting einstien's idea. light does not infinitely dilate time and we can prove that by the fact that it doesn't travel instentaneously. don't try to word twist out of this, you cannot both claim light having a non instintaneous velocity and an instintaneous one any more than i can claim 2+2 = 4 and not 4.

:lol: What? I'm not trying to "word twist" out of anything, and I haven't misinterpreted Einstein's idea (it was Lorentz's idea anyway, not Einstein's). There's some very funny people on this forum.

 

You still can't grasp that there are different frames of reference. Light moves at the same speed relative to every inertial observer, so of course it can't move instantaniously from any inertial frame of reference, it can't even slightly speed up. Light is infinitely time dilated and length contraction from its own frame of reference. It still wouldn't be moving instananiously, that's using infinite time dilation but ignoring length contraction. Space is infinitely lenght contracted as well so it's not moving at all in it's own frame of reference.

 

Read the opening post, I've completely reworded it. Stop as soon as you don't understand something and I'll explain it, then carry on until you get stuck again and I'll explain again.

Edited July 6, 2015 by A-wal

[Pmb]

Nope. I'm sure not lying. The fact that you think its funny is a result of one of either two causes; (1) you don't understand the physics well or (2) you understand the physics but you're one of those people who are unable to admit that they're wrong. I'd bet that's you since nobody is as ignorant as you've made yourself look in this thread about my example.

 

I'll explain it once more for the new comers and also to make it harder for A-wal to weasel out of admitting that he screwed up. Here we go yet again for the dishonest A-wal

 

Note: For the same of argument there are only two cars in the example. So when I say that no other cars are moving at 55 mph it means that I'm only speaking about the cars I'm using in my example. I'm also going to ignore general relativity. Although the results are the same I don't want to bother getting into it.

 

I've stated exactly what I meant above and I'm 100% right and A-wal is 100% wrong. And the fact that he can't admit it then it's very shameful act on his part. Let frame S be a road on which a car is moving in a straight line in the positive direction on the x-axis of a Cartesian coordinate system 55 mph. Also in frame S there is another care moving in the negative direction on the x-axis also at 55 mph. By definition of the problem; there are no cars moving at any other speed *** IN FRAME S *** than 55 mph.

 

That's all there is to it. Our little chum here doesn't fathom that there are only two cars in this problem by definition and that each car is traveling at 55 mph in frame S. Therefore by the assumptions of the problem there cannot be any car moving at any other speed other than 55 mph in frame S.

 

Sure, there could be other frames in which the speed of one of the cars will be traveling at 110 mph, but that won't be in frame S. And that's where A-wal keeps getting confused. He lacks the ability for focus on the statement of the problem and the statement of my conclusion which is identical and that's that in frame S there are no cars moving at any other speed than 55 mph.

 

Unfortunate for you folks the internet is flooded with people like A-wal who make mistakes that they can't correct due to their arrogance. In this case he thought he was being cute by making a sad attempt to prove that I was wrong by describing the problem from the rest frame of one of the cars. Unfortunately for him the problem stated that the cars are moving at 55 mph relative to the road and that was the point of the problem. Until A-wal is banned for his rude responses you'll have to deal with all of his deceptions, backpedaling and misunderstandings of physics. 

[A-wal]

:)

 

So I'm the one who's lying, making errors and trying to worm out of it but you're the one who just wrote an in depth attempt to worm out of the fact you made a very basic error. Although I wouldn't be at all surprised if someone with formal education in the subject made such big error, no physicist would ever say...

 

What you lack the understanding of is that it only applies to the equations of physics and not to physical reality. It's only treated as being equivalent mathematically. Every expert in relativity knows this and I know some of the best experts.

...that. If the mathematics don't describe reality then the mathematics are wrong. You're completely full of it. Go away.

[layman]

if you 2 take balls, each one with 1unit of inertial energy and accelerate them towards each other by adding 10 units of energy each, the amount of energy at the point of contact would be 20 units of accelerated energy.....lets leave out the original inertial energy, why wouldn't it be the same if they were moving away from each other?  it seems like common sense that if i were looking out the rear window of a car going 55mhp at a car moving away from me at 55mph it would look to me as if that car were moving at 110mph. the contraction at the front of the car is countered by the elongation at the rear of the car.

 

is it correct that if i am standing at one end of the road watching 1 car come at me at 55mhp while the other car is moving away from me at 55mhp, i would see the 1 coming at me as being faster and the 1 moving away as moving slower because the space between me and the car coming at me contracts and the space between me and the car moving away elongates but together they add up to 110mhp?

 

i'm sure everyone can tell i'm not formally educated, so please pardon me when i sound ignorant, it's only because i am.

 

can't motion be described in units of energy? if motion gets converted to energy then one can just track the energy and then figure the rest out.

[A-wal]

if you 2 take balls, each one with 1unit of inertial energy and accelerate them towards each other by adding 10 units of energy each, the amount of energy at the point of contact would be 20 units of accelerated energy.....lets leave out the original inertial energy, why wouldn't it be the same if they were moving away from each other?  it seems like common sense that if i were looking out the rear window of a car going 55mhp at a car moving away from me at 55mph it would look to me as if that car were moving at 110mph. the contraction at the front of the car is countered by the elongation at the rear of the car.

I don't know what you mean by the contraction at the front of the car is countered by the elongation at the rear of the car? Actually if two cars are moving at 55mph relative to the ground in opposite directions then they're moving away from each other at less than 110mph from their own frames of reference, very slightly. It's because light (all energy in fact but it's normally referred to as the speed of light) moves at the same velocity relative to all non-accelerating observers. There's an equivalence between mass and energy but they don't propagate through spacetime in the same way. If we raise the speed of the cars to half the speed of light relative to the ground then the two cars are moving away from each other at the speed of light from the ground's frame of reference at 0.8 the speed of light from the car's frame of reference. If a beam of light is shone from the Earth past a ship that's moving away from it at half the speed of light and then passes a second ship that's moving away from the first one at half the speed of light in the same direction the light moves away from the Earth at the speed of light, then past the first ship at the same speed, and then past the second ship at the same speed again despite the difference in their relative velocities.

 

The reason this makes sense is because they don't agree on the measurement of length in space (the straight line between them) or of a given length in time. Velocity is measured as distance over time so time dilates and length contracts so that an object that's moving away is moving across less space and taking more time to do it from the perspective of the intertial (not accelerating) observing doing the measurement. Because it's distance over time and both are changing in a way that lowers relative velocity, it means that the amount of time dilation and length contraction are very low unless objects are moving at a high fraction of the speed of light where it rises sharply. If only one dimension was effected then it would be a straight line progression so at half the speed of light it would be either half the length of space (length contraction) or twice the length in time (time dilation) to keep the speed of light the same. The upshot is that the first ship is moving away from the Earth at half the speed of light, the second ship is moving in the same direction and away from the first ship at half the speed of light but the second ship is moving away from Earth at 0.8 the speed of light and light is moving away from all three at the same velocity.

 

You can use the frame of reference of any inertial observer. So from the perspective of the first ship, the second ship is length contracted and time dilated but from the perspective of the second ship, the first ship is length contracted and time dilated so you could argue that it's purely subjective and not a real effect. But the speed of light isn't constant for accelerating observers. It slows down the harder they accelerate but an accelerating observer can never catch up to the same of light because it takes more energy to close the gap by the same amount the closer they get to the speed of light and approaches infinity as they approach the speed of light. It happens in exactly the same way as the velocity of a massive object can never reach the speed of light relative to other massive objects and the closer they get to it, the less difference the same amount of energy makes in their relative velocity the closer they get to the speed of light. This is why an object's mass increases as its relative velocity increases, E=mc^2. The upshot of this is that time dilation becomes a real and objective physical effect for accelerating observers in that less time will have passes for them than for inertial ones, as in the twin paradox.

 

It's all very pretty. Read the opening post of this topic. It should help.

 

is it correct that if i am standing at one end of the road watching 1 car come at me at 55mhp while the other car is moving away from me at 55mhp, i would see the 1 coming at me as being faster and the 1 moving away as moving slower because the space between me and the car coming at me contracts and the space between me and the car moving away elongates but together they add up to 110mhp?

No. There would be Doppler shift to take into consideration because one is moving away from you so its light waves get stretched out and one is moving towards you so its light waves get squashed up but everything I've described is what you get after Doppler shift has been taken into account and compensated for.