Relativity - my brain is hurting. Help !

Not a paradox but proof that using only mathematics to theorise observable phenomena is at best just a clunky and unimaginative language to transfere ideas. If you take the "observers" out of the equation and take into account what is being observed without observation you are left with a very simple example of perspective.   And what does perspective got to do with matter itself, nothing .

HI Don -

I believe the author is playing a word trick.

From a fixed observation point, as Observer A approaches the speed of light, his pocket watch runs slower, he and the pole become shorter, and their mass increases. But from Observer A's perspective, nothing appears out of the ordinary, including the size of the approaching barn.

IIRC, Einstein's Special Theory of Relativity starts with light traveling at a constant speed at all times. For example, light can not travel faster if you are shining a flashlight from a moving train. From that assumption, Einstein discovered that the only way for the rest of his math to work was to make matter and energy the same thing, and to have both space and time become stretchy.

ATB.

Hook

Relativity is not easy for humans to grasp intuitively. If it were, it wouldn't have taken until the early C20 for us to stumble across it.

The short answer to your question is that the apparent paradox exists because of the assumption of simultaneity. As soon as the assumptions (postulates) of relativity are accepted, they necessarily entail the loss of simultaneity. In other words, if you and I are in different frames of reference (e.g. by moving at different speeds), we will not perceive the same event as taking place at the same time. Does that fit with our everyday experience and, therefore, our intuition? No, but see my opening sentence.

So the barn-pole paradox (often phrased as a ladder-garage paradox without significant difference) is resolved once we realise that the event of the ladder being in the garage will not be perceived by the two observers as happening at the same time. Once we have that, the length perceptions sort themselves out.

Quoting Wikipedia may be the last refuge of an intellectual scoundrel, but I have to say that it does a pretty good job of this one: http://en.wikipedia.org/wiki/Ladder_paradox

Mark

Toby, Hook and Mark,

Thanks to all of you for your helpful responses. You have inspired me to read a bit more about Einstein's ability to describe the workings of our universe. As Ebor said, ( thereby confirming the reason for my brain hurting !), relativity is not easy to grasp intuitively.

I picked up on the concept of loss of simultaneity from your posts. I hadn't recognised that before.

With further reading I have begun to grasp the concept that, at close to the speed of light, not only do distances appear to shorten, but so does time (Hook's stretchy space and time ?). Leading to the concept that some things could move around the universe in (almost) no time at all ?

Or am I drifting off course here ?

Don.

Surely the fact that things APPEAR to be closer or are PERCEIVED to be of length different to actual length doesn't mean they are.

Maybe things could APPEAR to move around the universe in (almost) no time at all.

Taking a look into contemporary ideas on Relativity and Einsteins work is also an eye opener.  in 10 -20 years his core theories will be maybe thought of as historical rather than concrete. Matter and energy are the same ? No.      Matter can only go as fast as the speed of light -  but energy can travel far faster, we just don't have the technology to record just how fast it can go .

Fun stuff to think about, and it sounds like you've pretty much got it. 

Another paradox (maybe also in your book) is the "twins". Born together, one immediately goes for a 50 year ride in a very fast space ship. Upon the ship's return to earth, the 50 year old twin who stayed behind greets his long lost sibling...who is only 40 years old.  As Ebor said, the twins had different frames of reference, so they experienced time differently.

You're an aviation guy right? I think it was back in the early 1970's when scientist's placed an atomic clock on a jet aircraft and were first able to confirm time dilation (i.e., it ran ever so slightly slower than an atomic clock on earth).

Keep in mind that with his theories of relativity, Einstein was only trying to make sense of two very extreme situations: 1) speeds approaching that of light (a universal constant), and 2) a gravitational force so strong that one would need to achieve the speed of light in order to escape it.

But it would take an inconceivable amount of energy to propel a space ship close to the speed of light (i.e., mass increases with speed until eventually a near-infinite amount of energy is required for the space ship to go any faster). And I don't think anyone wants to get to close to the edge of a black hole. So for pretty much all practical purposes, the good old laws of Newtonian physics (where length and space and time are constants) still hold true.

We just have to remember to regularly adjust the clocks on the international space station. ;-)

I recommend Brian Greene's books on this sort of stuff. I'm no mathematician but found I could pretty much hang in with them-and theories of cosmology etc.The Fabric of Time maybe the best to start.

Bruce

We (Mrs D and myself) are just off for a hike (its my day off), so plenty of time to muse some of this most welcome feedback.

No doubt our walking speed will be our usual stroll at 4mph...........

...........or should that be 4x(1-(4x4/CxC)

Walk together at the same speed or you will age differentially...

Back. And she hasn't aged a bit. Me, on the other hand.......................

Do you have any links to peer refiewed science for this - or for both? I thought matter could never reach light speed? Why can energy exceed it?

Ooopps, I think I meant to write

4 x 1/ sqrt (1 - (4x4/CxC)), or at least something like that. !

Well as that famous scientist Meatloaf said "Objects in a rear view mirror may appear closer than they are" lol !!

That's right. October '71. Hafele and Keeting placed clocks on two commercial aeroplanes that flew around the world, one eastbound the other westbound. They compared the times on arrival back at Washington with a "stationary" clock. 

The planes flew at similar altitudes so the predicted gravitational effects (using Einstein's General Theory) on the airbourne clocks was considered to be similar with both of them speeding up slightly. The gravitational effect was estimated to be quite modest given the modest altitude compared with the earth's radius. The Westbound clock, moving Earth-speed minus plane-speed ran even faster, whilst the Eastbound clock travelling at Earth-speed plus plane-speed ran a bit slower and in fact slightly off-set the speeding up due to gravity.

The results were more or less in line with the predictions using Einstein's General and Special theories. I belive the experiment has been repeated a few times since then.

My renewed interest in the subject arose a few weeks ago when i was briefing a student on GPS and the need for the system to take into account the effects predicted by Einstein in his General theory (Gravitational) and his Special theory (Speed). The gravity wins in the satellites at c46 microseconds per day faster than Earth time over the c.7 microseconds per day slower for the speed effects (remember, the orbits of the satellites are inclined at about 55 degrees to the Equator). Overall, the satellite clocks run about 38 microseconds per day faster than the Earth clocks.

Yes quite right!  Matter and energy are effectively the same and the conservation of mass has to include energy in its stating - "e equals mc squared".  Or rearranging we get "m equals e divide by c squared", which was important at the time of the Big Bang, when massive amounts of energy were converted to mass.

The upshot of the 'Special Relativity (SR)' is

(1) That space and time are all one thing, they cannot be separated.  The Space-time continuum,

(2) The speed of light is constant (was known earlier but is a central core of SR) and this does not just mean that light will always travel at the same velocity in the same media - Oh no it is much more subtle than that.

I will try to explain:

If you are travelling in a train and throwing a ball to someone in your carriage in the direction of the travel of the train then it's speed is the throwing speed + train speed.  So if the train is doing 60mph and you throw the ball at 5mph, then to an observer outside the train the the ball is travelling at 65mph.  When your mate throws it back that will be 55mph.

This, however, is not true for light.  The velocity (speed/direction) of the light source and the observer are irrelevant, the speed of light from one to the other is always the same.  Not like our ball on the train at all.

This is difficult concept to swallow though!  But from this we have to say if the speed of light is constant then something else must 'change' and that something else is TIME.  This was the famous Einstein thought experiments on the tram in Switzerland.

(3)  OK!  All objects in the Universe travel at the speed of light through the Space-time continuum, you me, Tom Jones, The Moon etc.  We are all chugging along at the speed of light.  Crazy but true.

But objects like me and Tom Jones are travelling very slowly through space, most of our motion is through time.

Are you still with me?

OK So we build a big rocket and put such a powerful engine on it that we can approach a fair fraction of the speed of light.  So now we are traveling much quicker through space thus we have to be traveling slower through time.  Otherwise our speed through the space-time continuum would not be at the speed of light.

This is significant for satellites even, so GPS has to take account of it!

So we all have our own world view.  Every thing we see happened in the past.  When we look at the moon we saw what it was nearly 1.5s ago.

One thing that I should mention is that SR is formulated for objects moving at constant velocity - that's what the Special bit means - it's a special case.

Newtonian mechanics for most of the measurements we take are OK, but they are fundamentally flawed nonetheless.  For years astronomers were puzzled by the fact that the it gave an incorrect value for the position of Mercury when its light reached us by passing close to the Sun.

The other issue with Newtonian Mechanics is that they do not explain what gravity is, they give no clue.

That is where General Relativity comes in.

Meant to make a comment about energy travelling faster than light.  No way jose!  This could have only been said by someone who does not understand what energy is.  And what does far faster mean? Far is a distance not a speed.

If I have a couple of batteries and a piece of coal in my pocket will they occasionally zip off at FTL speeds?  Don't think so.

Bill, many thanks indeed.

Most of what you have explained, I can follow and (possibly) understand. But the bits above I am having difficulty with. Not difficult to believe - just difficult to grasp, imagine or understand. Probably because I am unaware of them in my everyday experiences.

I am (sort of) imagining a 4-dimensional version of my everyday 3-dimensional (very large) dining room. I can put all my effort into moving along the long wall (x), the short wall (y) or from the floor to the ceiling (z), or any combination of any two or three of these directions. But if I choose to "mix" the dimensions in which I move, my progress along any one specific dimension will be reduced.  Or.............I could stand still and simply move through time (I have a clock in the dining room and a watch on my wrist)? or, better still..........I could move through any combination of all 4 "dimensions" (with respect to my dining room and clock) in which case my progress through the TIME dimension (as displayed on my wrist watch) will likewise be reduced but not noticeably so unless I move through the other three dimensions at a very, very high (steady) speed. ?

The effects that need to be taken into account when using satellites for navigation eg the US GPS no doubt include an allowance for their clocks running more slowly due the satellites moving relatively faster than the equipment on earth. But I understand the satellite clocks also run faster than their earthbound twins because of this effect we call gravity ? How would that feature in my dining room experiment ?

Apologies if the above thoughts and questions are either naive or pointless. Just say so and I will try Bruce's recommended book first, then try to ask more meaningful questions later.

Bruce,

Did you mean "The Fabric of the Cosmos" ? which I understand deals with time and other aspects of the universe.

many thanks Don

For me, the really cool thing here is that the test results confirmed Einstein's math worked.

It's so easy to forget that when he made this prediction, all he had was paper, pencil and an incredible imagination. Wonder what he could have done if he were alive today, and had access to supercomputers and particle accelerators and such. How would he compare to today's greatest physicists?

Not that I'm a big boxing fan, but it's sort of a geek's version of what if Sugar Ray Robinson was alive today? Could he beat Floyd Mayweather?

Hi Don, you ask some hard to answer questions, especially in a forum where I can't sit you down and do a diagram.  btw your questions are spot on the money, I used to love students like you in my teaching days.  Seriously no sarcasm!

OK let's try.

From your reply I can see that you understand the movement of me and Riz Lateef through 4D space-time and you can see the consequence of us moving rapidly through space.

Now as to time dilation you are quite right, gravity is also important.  The greater the gravity then the slower the internal clock runs.  According to a certain Prof Hawkins inside a Black Hole time stops!  Now that is a difficult concept!

Now Einstein proposed that the gravity of a mass distorts space-time around in proportion to its gravitational constant and distance, so this distortion lessens as you move away from the object - ie inverse square law.  Now if we can imagine two objects A & B that are separated by a portion of gravity distorted space then light will travel from A to B at constant speed and will appear to cover a greater distance.  That is it will appear that the photons of light from A to B Are going faster than the speed of light.  This of course is not possible and again we realise that light speed is constant but time has slowed down within the distortion. 

See http://www.quora.com/How-does-gravity-affect-time for a nice diagram and a better explanation than mine.

From the figures I have seen GPS satellites internal clocks are effected more by their speed than by the lessening of the gravity they experience.  Remember if you are in orbit you become weightless, but not because of your distance from Earth but because you are constantly accelerating towards the Earth at 1g.  So you feel a force of 1g away from Earth.  Result the overall force you feel is 0g.  But although they are weightless they are travelling through space which is distorted due to its distance from the Earth.

Yes, that is the one.

Bruce

A bit off topic.

Hooks paradox concerning the 40 year old twin who travelled the universe for 50 years reminded me of the Stanislaw Lem novel "Return From The Stars". The lead character returned to earth after 127 years, having only aged 10. Probably my favourite Lem novel, well worth a read.

Back on topic.

Is the so called 40 year old space traveller really only 40 year old. Is he not a 50 year old with a very inaccurate time piece.

I was going to ask the same (or similar) question Frank.

Does the human body and its metabolism actually slow down to match the dilated time. I appreciate that an atomic clock does, but i'm unclear about biological processes.

Secondly, what is the "traveller's perception of the people left on Earth, who, according to the traveller's frame of reference, are moving away from him ?

Just when i thought the headache was easing....................??????????????