Relativity Made Simple

[A-wal]

The basic principle of relativity was put forward by Galileo well before the special and general theories of relativity were formulated. It states that there's no distinction between object A moving while object B is at rest and object B moving while object A is at rest. In other words it doesn't make sense to say that an object is moving through space because you need to compare it to another object to make that determination. All you can say is that the objects are moving relative to each other.

 

Special relativity builds on the concept of Galilean relativity to explain how light can move at the same speed relative to every non-accelerating (inertial) observer. If an object is moving towards you at half the speed of light and it shines a light in front of it then that light will move past you at the speed of light rather than 1.5 times the speed of light, so you'd measure it moving away from the other object at 0.5 the speed of light but it will be moving away from the other object at the speed of light as measured by them, so they'd measure it moving towards you at 1.5 times the speed of light.

 

Either object can be viewed as the one that's moving so from the other object's perspective you're moving towards them at 0.5 the speed of light and if you shine a light in front of you they'd measure it as moving away from you at half the speed of light and you'd measure it moving towards them at 1.5 times the speed of light but light always moves at the same speed relative to any inertial observer so you'd measure it moving past you at the speed of light and they'd measure it moving away from themselves at the speed of light.

 

If the light is moving away from the other object at the speed of light as measured by them and they're moving towards you at 0.5 the speed of light then under normal circumstances you'd expect the light to be moving past you at 1.5 times the speed of light. The only way it can make sense for two observers to measure any difference in the amount of space that the same light moves through in a given amount of time is if they measure distances in space or time differently to keep the speed of light the same relative to both of them.

 

Time and space are shortened (time dilation and length contraction) from your perspective so that the distance the light is traveling and the amount of time it's taking to do it are reduced so that instead of moving past you at 1.5 times the speed of light it moves past you at the right speed, the speed of light. From their perspective time and space are shortened so that the distance the light from you is traveling away from you and the amount of time it's taking to do it are reduced so that they see your light moving past them at the speed of light.

 

This means that each will perceive the other as moving slowly through time and as lengthened in the spacial dimension that they're moving relative to each other. So if two ships pass each other at half the speed of light each will view the others ship and anything on it including the crew as moving in slow motion and stretched in the direction of relative motion, because each ships own perspective of space and time are shortened relative to the other ship but they perceive themselves as unchanged, which means each ship has to perceive the other ship as lengthened in time.

 

This means that an object moving relative to the observer won't be accelerated as much as the observer would be using the same amount of energy, because the other object is moving through a greater distance in space from the observer's perspective and is moving slowly through time as well, so the other object's mass increases as its relative velocity increases and the relationship between the only four things in the universe (energy, mass, time and space) is energy is equal to an objects mass times the speed of light (speed is just distance in space over time) squared, E=mc^2.

 

That's the whole of special relativity in seven very short paragraphs. One really nice way of looking at it is that every object is moving through spacetime at the speed of light. Every inertial object is at rest from it's own perspective so every observer and anything at rest relative to them are moving through time at the speed of light and other objects are moving slower through time as their relative velocity increases so that every object is moving through spacetime at the speed of light from every observer's perspective.

 

Special relativity doesn't describe acceleration but here it is anyway. If an observer accelerates to the same relative velocity as an object that's moving at half the speed of light from the observers initial frame of reference then then the observer is moving into a frame in which it was time dilated and length contracted before it accelerated and so less time passes from the perspective of accelerating objects than it does for inertial ones. The upshot is you can get to anywhere in the universe in as little time as you like because time dilation and length contraction will bring distant objects towards you as you accelerate.

 

Light does slow down relative to accelerating objects but never enough that they can keep up with it. This is because the same increase in acceleration makes less of difference to the velocity that light moves relative to the accelerator the harder they're accelerating, in exactly the same way that the same amount of acceleration makes less difference to an objects velocity relative to other objects the higher the velocity is between the observer and the object. Acceleration is to light (all energy) as velocity is to mass, the relationship is identical.

Edited June 8, 2015 by A-wal

[phillip1882]

okay let's say i have two light beams. i fire them toward each other. clearly they would cover the necessary distance in half the time of firing a single light beam to the location of the first. if velocity is distance over time, this would mean, from the perspective of the light beams, the oncoming light beam is traveling twice the speed of light.

[Moontanman]

okay let's say i have two light beams. i fire them toward each other. clearly they would cover the necessary distance in half the time of firing a single light beam to the location of the first. if velocity is distance over time, this would mean, from the perspective of the light beams, the oncoming light beam is traveling twice the speed of light.

 

 

I'm pretty sure that perspective is only valid for a third observer...

[A-wal]

okay let's say i have two light beams. i fire them toward each other. clearly they would cover the necessary distance in half the time of firing a single light beam to the location of the first. if velocity is distance over time, this would mean, from the perspective of the light beams, the oncoming light beam is traveling twice the speed of light.

You can't really view it from the perspective of the light beam because travelling at the speed of light would make then infinitely time dilated from their own perspective, so it wouldn't take any time at all and the whole universe is a singularity from the perspective of energy, including a light beam. Relativity is more about the perspective of massive objects that can never reach that speed relative to other massive objects regardless of how much they accelerate, and they can't even begin to catch it because it always moves at the same speed relative to all inertial objects, although you can slow it down by acceleration. In a sense you can define acceleration as velocity relative to energy.

 

It is true that two objects could move away from a third object at 0.6 for example in opposite directions and therefore be moving away from each other at 1.2c from the perspective of the third observer, but that's okay, as long as no two objects reach the speed of light relative to each other.

 

I just want to make something clear. I don't entirely agree with relativity as it's described, but this thread has nothing to do with that. Everything in the opening post was the things that the standard version and the way I think it works have in common (mainly special relativity) and I want to keep it that way in this thread.

[Guest MacPhee]

Suppose you have two persons, A and B, standing on Earth. They're both the same age, say 30.

 

A gets into a starship, which heads for Alpha Centauri at .9999999 light-speed, reaches the star, loops round it, travels back to Earth, decelerates, and lands back on Earth again. A gets out.

 

He's welcomed back by person B, who has hung around patiently awaiting A's return. For 9 years.

 

As a result of this 9 year wait, B is naturally now 39. But we're supposed to accept that the other guy A - the star-traveller - is still only 30! Even though all A did was travel about a bit!

 

Is that really plausible?

Edited February 22, 2013 by MacPhee

[A-wal]

Yes it is. It's not only plausible, it's how it has to work. Everything is travelling though space-time at the speed of light. If you're an intertial object then you're not moving though space at all and moving through time at the speed of light from your own perspective, and the same applies to any object at rest relative to you. If an object is moving though space at a constant velocity relative to you then it's moving through time at less than the speed of light to keep its overall velocity at the speed of light. This situation is symmetric though because they would see you moving through space at the same rate as you observe them moving through, and the same applies to time so that you're moving through space-time at the speed of light from their perspective as well.

 

In your example person A can't reach the speed of light from the perspective of person B back on Earth. Let's say that person A accelerates to half the speed of light, then accelerates by exactly the same amount again. Now, length contraction and time dilation mean that person A didn't accelerate by as much as they did during the first acceleration despite using the same amount of energy. This is why an objects mass increases as its relative velocity increases. Object As mass didn't increase from it's own perspective of course. After the first burst of acceleration it became inertial again, but length contraction and time dilation mean than it finds itself in a new frame of reference where time and space in the dimension that it accelerated in are now shorter than they are from Bs perspective, but of course the situation is symmetric, so how can that be true?

 

I'm going to have to bring in a third object to explain this. Object C is some distance away from Earth in the same direction that A accelerated in so that you can draw a straight line through all three objects and object C is at rest relative to Earth. The distance between object B and object C is less from object As perspective than it is from the perspectives of objects B and C. If there were another object in the same straight line at rest relative to object A and some distance away from it then that distance would be less in the object B and object Cs frame than it is in the frame of object A and the other object.

 

The second burst of acceleration from object A accelerates it just as much as the first did from its own perspective, but in space that's length contracted and time that's dilated from the perspective of its original frame. This means that A is travelling through space at a different velocity from it's own perspective than it is from the perspective of object B and the difference increases the more it accelerates in total, and because all objects travel through space-time at the speed of light it means that it's travelling through time at a different rate than it is in object Bs frame which is responsible for the difference in age when A returns to Earth. Because object A is doing all the accelerating it means that when it gets back to Earth it's ended up in a frame where it was moving through space and therefore not moving as quickly through time.

 

 

Btw gps satellite have to take relativity into account or they slowly go out of sync with Earths time.

 

Hope that helps.

Edited February 23, 2013 by A-wal

[A-wal]

I've rewritten this and edited the opening post. I'll put the original down here.

 

 

Relativity Made Simple (I hope)
If an object is stationary (inertial (not accelerating)) in space and it sees another object coming towards it at half the speed of light then you could just as easily say that it's moving towards the other object at half the speed of light and the other object is stationary. There is no distinction between which one is moving. The only statement you can make is that they moving towards each other at half the speed of light. All the laws of physics remain the same in any inertial frame, meaning all frames are equal and no frame can be said to be unique in any way. Having said that, you could use the cosmic background radiation as a frame of reference for all others, but you could do that with any frame of reference. If you're in a car and you throw a ball into the air then it doesn't go flying backwards because the laws in all non accelerating frames are the same, including the speed of light. You can't measure your speed relative to light because you'll always get the same answer of 186,000 miles per second. So if two objects are heading away from Earth at different relative velocities and you shine a flash light then the light beam will pass both of them at the same speed, meaning all three observers measure time and space differently to keep the speed of light the same for all of them. Velocity is just a measurement of distance over time. There's one spacial dimension involved because you can always draw a straight line between any two objects, and time. Both shorten from the perspective of an accelerating observer to keep the speed of light constant. This is called length contraction and time dilation. They're caused by the fact that energy has to travel different distances from the perspective of two observers in motion relative to each other, and the difference is length contraction and time dilation.

 

If a ship were flying away from Earth and a signal was sent from Earth to the ship and from the ship to Earth then would both signals take the same amount of time to reach their destination? Yes, but both Earth and the ship would say no. Both observe outgoing signals taking longer than incoming signals because outgoing signals have to catch up to the receding destination. Outgoing signals have to travel further and take longer than incoming ones do to make the same journey, because outgoing signals are measured to when they arrive while incoming signals are measured from when they're released. Signals sent by the other observer would be travelling a shorter distance and wouldn't take as long to reach the destination as a signals sent from themselves to the other observer because outgoing signals are travelling to where an object is going to be and incoming signals are travelling to where an object is and the difference is length contraction and time dilation. Objects are always travelling through space-time at the speed of light from all frames of reference. In your own frame your stationary and moving through time at the speed of light. Objects also see other objects with a different relative velocity moving at the speed of light because they're moving through time slower (time dilation) from each others perspective and their total velocity through space-time will always equal the speed of light.

 

Imagine two ships moving at different velocities, both with a light beam moving up and down between the ceiling and the roof. It takes one second for the light to travel up or down from mirror to the other. Each would see the light on the other ship move in a zigzag as its relative velocity is added to the lights vertical motion. Light doesn't speed up to make up the difference, so it takes longer than one second for the light to get from one mirror to the other on the others ship from both perspectives. A second for either is a shorter amount of time than a second for the other, so each sees the other moving in slow motion because the light on the other ship has further to go. Now one is stationary relative to a tunnel which the other ship travels though. The ships front end comes out one second after its back end enters, but space is length contracted in the direction that it's travelling in, making anything in the other frame including the tunnel length extended by comparison. Its front end emerges before the back end enters from the perspective of the ship at rest relative to the tunnel. From this frame, the ship is longer than the tunnel.

 

If you (A) flew away at half the speed of light while your twin (E) stayed on Earth then you would change your frames of reference relative to each other. You're always stationery from your own perspective and light is always moving at the same velocity ©. Everything else is relative. From both perspectives the other will be travelling at 0.5c but each sees themselves as stationary. A travels one light-year in two years, but a light-year has changed from As perspective relative to Es because they've moved into a different frame where the speed of light is the same relative to both of them despite their different relative velocities. It moved further from As perspective in the time it took for the light to get one light-year from Earth from Es perspective and the same is true from As perspective of E. So the distance that the other ship covers wont seem like far enough from each perspective over any given unit of time, and if the distance that the other is covering decreases then the space and time separating them must decrease by an equal amount split evenly between the two (there's one time and one spatial dimension as we're moving in straight lines to keep things simple). The measurement of the others space-time has lessened because the other ships time will appear to be in slow motion (time dilation) and there will appear to be less space (length contraction) along the one spatial dimension (straight line) that they are moving from the perspective of both frames and lengthens each ships perception of anything in the others frame, which keeps the speed of light constant from the perspective of both frames. This removes the discrepancy of the speed of light from the persecutive of different relative velocities because it isn't travelling as far in space or in time, and therefore as fast as in other frames as it would if it wasn't for length contraction and time dilation, and bringing it right back to c relative to every frame of reference.

 

Everything up until now has been symmetric, so each twin sees the same affects on the other, and in exactly the same way. The twin paradox (not actually a paradox at all) is that the one leaving Earth will be younger than their twin when they return. To start with we'll give both twins a rolling start and finish. The twins pass Earth moving in opposite directions at just over half the speed of light relative to an observer on Earth who sees them moving away from each other at over the speed of light, which is fine as long as no one sees themselves moving above light speed relative to anyone else. Each twin sees themselves moving at just over half light speed relative to Earth (Earth sees them moving at that speed so the same must be true in reverse) and each twin sees the other moving at below light speed because of length contraction and time dilation. But this isn't a real affect because each sees the other one moving in slow motion and length extended (because the space is contracted), which stops anyone from moving faster than light relative to anyone else. When they turn round they have to accelerate in the opposite direction (there's no such thing as deceleration in relativity because it's just acceleration in the opposite of some arbitrary direction). If one is at rest and the other accelerates and comes back then it becomes a real affect and one twin is literally younger than the other one.

 

A uses one unit of energy to travel up to half the speed of light relative to E. A is now static in its new frame of course. A then uses another unit of energy to again reach half the speed of light relative to an object in its new frame. From Es frame that second unit of energy didn't accelerate A as much as the first one did, but from As perspective it did because of length contraction and time dilation. So if the same energy is needed to move over a relatively smaller amount of space-time then the mass of A has increased from Es frame, and Es has from As frame as well. So the others energy requirement to accelerate increases from both perspectives as their velocity relative to each other increases, so your mass increases the faster you move relative to something else from their perspective. Energy becomes mass as you accelerate relative to the speed of light from the perspective of other frames of reference. That's how matter and energy are interchangeable, E = mc^2. What separates them is the fact that A has accelerated and E hasn't. If E were to accelerate into As new frame then they'd be the same age again. Length contraction and time dilation would lessen as their speeds become relatively closer to each other. When their relative velocities match they'll be in the same frame again and the only apparent time lag will be caused by how long it takes for light to cover the distance separating them (light hours/days/years).

 

You can effectively travel as fast as you like, there's no such thing as absolute velocity and there's no speed limit because you will be in a new frame every time you stop using energy to accelerate and the speed of light and your energy requirement for acceleration relative to c is always the same in every possible inertial frame. You can go anywhere in as short an amount of time as you like if you have enough energy, it's just that objects can't reach the speed of light relative any other objects, so space and time make up the difference by being relative rather than fixed. If you accelerated to half the speed of light from your starting frame then you'd be in a new frame when you stop accelerating and you'd now be static from your own perspective and the energy requirement to accelerate to half speed of light would be the same as it was in your starting frame. If accelerated again up to half the speed of light relative to an object in your new frame then you wouldn't be travelling at the speed of light from your starting frame because you are length contracted and time dilated from the perspective of your starting frame and so you're moving slower through time and space. Time and space aren't fixed. As you accelerate towards something, it gets closer to you beyond what you would expect from the increased velocity. You can move infinitely fast, but as far as the rest of the universe is concerned you can't. So if you were to accelerate away from Earth and then return, you would be younger than your twin who stayed home because you were travelling slower through time and space from Earths perspective.

 

Gravitys strength is directly proportional to mass and inversely proportional to the square of the distance to the mass. That just means that its strength is divided by four if the distance is doubled and multiplied by four if the distance is halved. In zero dimensions (point/singularity) would be infinite. In one spatial dimension (straight line) its strength would remain constant over any distance. In two spatial dimensions (flat plane) it would be directly proportional to the distance. In three spatial dimensions it's an inverse square. It's proportional to the space it fills. We feel our own weight on Earth but it's not gravity that we feel, it's the electro-magnetic force between the atoms that are resisting gravity and pushing us upwards by the same amount that gravity is pulling us down. Neutron stars are heavy enough to collapse past this resistance and are held up by the resistance of the neutrons. Black holes are so heavy for their size that nothing can hold them up and they collapse completely. We feel the difference in the amount of force being applied to our points of contact with the ground and the rest of our bodies, which is why it's more comfortable when this difference is spread over a larger area when we lay down. The difference in the strength of a gravitational field is also all that can be felt rather than the strength of the field itself, because it's relative. The relative difference in the strength of gravity is called tidal force. On Earth that difference is very small and can't be felt but in a strong enough gravitational field it's enough to rip solid objects apart.

 

Relativity explains how electricity and magnetism are actually the same force (electro-magnetism). A magnetic field can turn into an electric field if you accelerate relative to it because length contradiction moves the electrons closer together giving the field a negative charge, so the magnetism from the previous frame is felt here as electricity.

Edited June 8, 2015 by A-wal

[Pmb]

When you fire two beams of light at each other its the "relative" change in distance between two objects. But that's not how velocity is defined. The velocity of an object is defined as its change in position relative to a particular frame of reference. E.g. a car can travel at 55 mph relative to the road. 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. The only thing having to do with 110 mph is the distance between the two objects is changing at a rate of 110 mph. But one can't change to a frame in which one of the beams of light is at rest and measure the speed of the other beam.

 

Note that the principle of relativity alone cannot be used to show that the speed of light is invariant. One needs a separate postulate for that. The second postulate used by Einstein was simply that, i.e. the speed of light is invariant. Another way to phrase it is that the proper mass of a photon is zero.

Edited June 22, 2015 by Pmb

[A-wal]

What are you taking about?

 

You can use either the car or the road as a frame of reference. Using the road's frame there's two objects moving away from each other at 110 mph but using either of the car's frames the other car is moving away at slightly under 110 mph because of time dilation and length contraction.

 

Of course you can't change to a frame where one of the light beams is at rest. You can't even slow them down using inertial frames, that's the whole point, that the speed of light is the same in every inertial frame. But you can slow the speed of light by using an accelerating frame of reference.

 

Yes, the invariant velocity of light relative to every inertial observer is a postulate and the special theory of relativity describes its implications, so of course you can show that the postulate is accurate using relativity alone, by testing it's predictions.

Edited June 13, 2015 by A-wal

[A-wal]

"But you can slow the speed of light by using an accelerating frame of reference"...

 

And the way accelerations add together so that a second increase in acceleration (using the same increase in energy as the first) won't slow light relative to the frame of reference of the accelerator as much as the first increase of acceleration did is identical to the way that two acceleration bursts using the same amount of energy to change the inertial frame of reference of an observer so that their velocity relative to objects that were initially at rest with respect to the accelerator doesn't increase their velocity relative to each other as much as the first acceleration burst did.

 

So acceleration is to the relative velocity of energy as relative velocity is to mass.

[phillip1882]

there's so much wrong with htis post i don't even know where to begin.

 

"You can't really view it from the perspective of the light beam because travelling at the speed of light would make then infinitely time dilated from their own perspective, so it wouldn't take any time at all and the whole universe is a singularity from the perspective of energy, including a light beam."

ummm no. light takes a fixed amount of time to travel any distance. that is measurable. therefore time is not infinitly dilated. if it was, light could travel instintaneously.

 

"Relativity is more about the perspective of massive objects that can never reach that speed relative to other massive objects..."

i somewhat agree, except its quite possible to have two objects going faster than the speed of light realtive to eachother, even if they cannot reach the speed of light.

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 eachother? if you say anything other than 120% of the speed of light, clearly you don't understand basic math.

[A-wal]

there's so much wrong with htis post i don't even know where to begin.

Yea okay. :)

 

"You can't really view it from the perspective of the light beam because travelling at the speed of light would make then infinitely time dilated from their own perspective, so it wouldn't take any time at all and the whole universe is a singularity from the perspective of energy, including a light beam."

ummm no. light takes a fixed amount of time to travel any distance. that is measurable. therefore time is not infinitly dilated. if it was, light could travel instintaneously.

Um what? Distance is relative. Light takes a variable amount of time to travel between any two objects depending on the relative velocity of the observer to those objects. 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. You obviously don't understand what you quoted or how relativity works so you really shouldn't be trying to correct others before learning it yourself. It's also very dificult to take someone who doesn't use capital letters seriously. How old are you?

 

"Relativity is more about the perspective of massive objects that can never reach that speed relative to other massive objects..."

i somewhat agree, except its quite possible to have two objects going faster than the speed of light realtive to eachother, even if they cannot reach the speed of light.

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 eachother? if you say anything other than 120% of the speed of light, clearly you don't understand basic math.

It is true that two objects could move away from a third object at 0.6 for example in opposite directions and therefore be moving away from each other at 1.2c from the perspective of the third observer, but that's okay, as long as no two objects reach the speed of light relative to each other.

Clearly you don't even understand basic English. I'd try to get the hang of that first before you start trying to tackle scientific topics.

Edited June 19, 2015 by A-wal

[phillip1882]

Um what? Distance is relative. Light takes a variable amount of time to travel between any two objects depending on the relative velocity of the observer to those objects. 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. You obviously don't understand what you quoted or how relativity works so you really shouldn't be trying to correct others before learning it yourself. It's also very dificult to take someone who doesn't use capital letters seriously. How old are you?

 

what the heck does grammer have to do with anything? can you understand what i'm saying? if yes, then we're communicating.

i'm 32, no i don't like have to try to captialize every sentence on the internet. as long as my mesage gets across, that should be enough.

let's start from the beginning.

the velocity of light is constant form every inertail frame of referance correct?

what is this velocity?

what is 60% of this velocity?

imagine we have 4 objects ABCD. A and D are stationary realtive toward eachother.

we agree it possible to go 60% of the speed of light, object B travel 60% of the speed of light away from A toward D, object C travels 60% of the speed of light away from D toward A. what is the velocity of B relative to C from the persective of C?

[Pmb]

"What are you talking about?" - What a shame. It was so clear too. I was talking about observations being made ***in the frame of reference of the -->road<---*** and in that frame there is nothing moving at 110 mph with respect to the road. Please read more carefully next time and perhaps you'll understand.

[sanctus]

Admin notice: A-Wal any more "rude and offensive"-behaviour like in post 12 and you'll be banned. Please see http://www.scienceforums.com/index.php?app=forums&module=extras&section=boardrules for our rules (link is also on the bottom right on each page).

[A-wal]

Sorry I tend to lower myself to the level of whoever I'm dealing with. I should get out of that habit because it doesn't do me any favours. I was merely responding in kind to the rude and disrespectful comments of others. Aren't you going to warn them as well?

 

the velocity of light is constant form every inertail frame of referance correct?

 

what is this velocity?

 

what is 60% of this velocity?

 

imagine we have 4 objects ABCD. A and D are stationary realtive toward eachother.

we agree it possible to go 60% of the speed of light, object B travel 60% of the speed of light away from A toward D, object C travels 60% of the speed of light away from D toward A. what is the velocity of B relative to C from the persective of C?

"the velocity of light is constant form every inertail frame of referance correct?"

Of course.

　

"what is this velocity?"

Roughly 186,000 miles per second, but it's irrelevant because it would work in exactly the same way with any velocity. Its value is arbitrary and independent of the effects of relativity. It's the fact that it's the same in all inertial frames of reference that matters. There's no need to specify the actual velocity of light.

　

"what is 60% of this velocity?"

0.6c

　

"imagine we have 4 objects ABCD. A and D are stationary realtive toward eachother.

we agree it possible to go 60% of the speed of light, object B travel 60% of the speed of light away from A toward D, object C travels 60% of the speed of light away from D toward A. what is the velocity of B relative to C from the persective of C?"

 

You're asking what velocity two objects moving at 0.6 in opposite directions along the same axis from the perspective of a third object would measure relative to each other from their own frames of reference. So that's just the same as object X accelerating away from object Y until it reaches velocity of 0.6c relative to object Y and then accelerating by the same amount again, so 0.6c + 0.6c. I think it's roughly 0.8c but I don't have the formula to give an exact answer.

Could someone please post this formula. I can't find it and I need it to check what I posted in the relativity wheel topic.

　

You claimed "there's so much wrong with htis post i don't even know where to begin" and then gave these as examples.

 

1

""You can't really view it from the perspective of the light beam because travelling at the speed of light would make then infinitely time dilated from their own perspective, so it wouldn't take any time at all and the whole universe is a singularity from the perspective of energy, including a light beam."

ummm no. light takes a fixed amount of time to travel any distance. that is measurable. therefore time is not infinitly dilated. if it was, light could travel instintaneously."

 

Light does not take a fixed amount of time to travel any distance. It takes a variable amount of time depending on the relative velocity of the observer doing the measurements. Light does travel instantaneously in the sense that it moves at the speed of light from any inertial frame because time dilation and length contraction approach infinity as relative velocity in an inertial frame of reference approaches the speed of light.

 

2

""Relativity is more about the perspective of massive objects that can never reach that speed relative to other massive objects..."

i somewhat agree, except its quite possible to have two objects going faster than the speed of light realtive to eachother, even if they cannot reach the speed of light.

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 eachother? if you say anything other than 120% of the speed of light, clearly you don't understand basic math."

 

I'd already said: "It is true that two objects could move away from a third object at 0.6 for example in opposite directions and therefore be moving away from each other at 1.2c from the perspective of the third observer, but that's okay, as long as no two objects reach the speed of light relative to each other."

 

Please continue. If there's so much wrong with what I wrote that you "don't even know where to begin" then I must have made loads of mistakes. Please enlighten me.

 

 

"What are you talking about?" - What a shame. It was so clear too. I was talking about observations being made ***in the frame of reference of the -->road<---*** and in that frame there is nothing moving at 110 mph with respect to the road. Please read more carefully next time and perhaps you'll understand.

I suggest you start following your own advice. The cars are moving away from each other at 110mph with respect to the road so that statement isn't true.

 

I understood you perfectly and I answered your misconceptions. "You can use either the car or the road as a frame of reference. Using the road's frame there's two objects moving away from each other at 110 mph but using either of the car's frames the other car is moving away at slightly under 110 mph because of time dilation and length contraction."

 

Better sanctus? :)

Edited June 22, 2015 by A-wal

[CraigD]

You're asking what velocity two objects moving at 0.6 in opposite directions along the same axis from the perspective of a third object would measure relative to each other from their own frames of reference. So that's just the same as object X accelerating away from object Y until it reaches velocity of 0.6c relative to object Y and then accelerating by the same amount again, so 0.6c + 0.6c. I think it's roughly 0.8c but I don't have the formula to give an exact answer.

Could someone please post this formula. I can't find it and I need it to check what I posted in the relativity wheel topic.

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.