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General Science => General Science => Topic started by: Chuck F on 30/01/2011 20:07:12

Title: If the speed of light is constant, time must be constant too?
Post by: Chuck F on 30/01/2011 20:07:12
The theory of relativity states that everything is relative to the observer. I understand that and it makes sense.  The problem I have is that say you have 3 planets

      (a)                  (b)                   (c)

Planets (a) and (c) are moving away from each other at just under the speed of light.  Planet (b) is always halfway between them.  According to reletivity an observer on planet (a) would see time neary stopped on planet (c) and slowed down to 1/2 on planet (b).  But an observer on planet (c) would see time nearly stopped on (a) and 1/2 on (b).  Planet (b) would see time being 1/2 on both (a) and (c) ie time would appear to be the same on both planets.  This is due the the fact we are observing the light and because the distance is changing it is stretching the observed time and slowing it down.  In reality time has passed the same on all 3 planets.  The same would hold for the person on the event horizon of a black hole.  We would observe him as if time had stopped.  but he would observe us the same.  Because to him we are moving away at the speed of light.  The speeding up or slowing down of time only occurs because the speed of light is constant therfore the time appears squished or stretched.  So if we sent a ship to a planet 10 light years away at 1/2 the speed of light it would take 40years round trip they would age 40 years we would age 40 years both planets would age 40 years.  It would appear that it took them 30 years to get there but only 10 to get back.  In reality it takes 20 years both ways.

I could very well be wrong on this but every thing I have seen on reletivity is from the point of view of the observer.  And from the observers stand point time is not constant. But the actual time passing is constant.
Title: Re: If the speed of light is constant, time must be constant too?
Post by: graham.d on 31/01/2011 16:39:29
It is more complicated than you realise, Chuck. I could explain, but it would be easier if you got a book on special relativity from the library. The time dilation effects are not simply because of the Doppler effect on light. You also have to do the maths more rigorously. The nearest problem to the one you describe is referred to as the "Twin Paradox" (it is not actually a paradox but it can seem that way until you understand Special Relativity); you can find lots of references and explanations on the internet.
Title: Re: If the speed of light is constant, time must be constant too?
Post by: Bored chemist on 23/09/2018 14:14:17
It has been determined that the "speed of light" is not constant.
What would your second guess be?
Title: Re: If the speed of light is constant, time must be constant too?
Post by: Janus on 23/09/2018 17:41:43
The theory of relativity states that everything is relative to the observer. I understand that and it makes sense.  The problem I have is that say you have 3 planets

      (a)                  (b)                   (c)

Planets (a) and (c) are moving away from each other at just under the speed of light.  Planet (b) is always halfway between them.
According to who?   The problem is that if Planet B says that it is always a equal distance from Planets A and C, neither planet A or C will agree to that statement.
Quote
According to reletivity an observer on planet (a) would see time neary stopped on planet (c) and slowed down to 1/2 on planet (b).  But an observer on planet (c) would see time nearly stopped on (a) and 1/2 on (b).  Planet (b) would see time being 1/2 on both (a) and (c) ie time would appear to be the same on both planets.
Your numbers are quite a bit off.  Let's assume that A and C are traveling at 0.999998999c relative to each other, as measured by either A or C, then they will measure the other's clock as ticking at ~1/100 as fast as their own.  If we also assume that B remains halfway between A and C as measured by B, then B measures the relative velocity between itself and either of the other two as being 0.999c (not) 1/2 of 0.999998999c)    A and C will also measure this as being their relative speed relative to B.   B will measure clocks A and C as ticking 1/22 as fast as it own, and A and C will measure clock B as ticking 1/22 as fast.
  This is due the the fact we are observing the light and because the distance is changing it is stretching the observed time and slowing it down.  In reality time has passed the same on all 3 planets.  The same would hold for the person on the event horizon of a black hole.  We would observe him as if time had stopped.  but he would observe us the same.  Because to him we are moving away at the speed of light.  The speeding up or slowing down of time only occurs because the speed of light is constant therfore the time appears squished or stretched.  So if we sent a ship to a planet 10 light years away at 1/2 the speed of light it would take 40years round trip they would age 40 years we would age 40 years both planets would age 40 years.  It would appear that it took them 30 years to get there but only 10 to get back.  In reality it takes 20 years both ways.

I could very well be wrong on this but every thing I have seen on reletivity is from the point of view of the observer.  And from the observers stand point time is not constant. But the actual time passing is constant.

You appear to be confusing Relativistic effects with the observation of Doppler shifting.
While you do visually see a clock moving away from you as ticking more slowly due to the fact that the distance is increasing, you also would see a clock coming at you to run fast due to the decreasing distance.   
However, in most discussions of Relativity, we assume that we have accounted for this, and are only considering what is "left over".
For example, if you are looking at a clock that is one light hour away and at rest with respect to you, the light you are seeing "now" left 1 hr ago.  So if you see the clock read 12:00, you know that it actually reads 1:00 at that moment.
So, generally, when dealing with Relativity, we would say that you measure the clock as reading 1:00, even though you are visually seeing it read 12:00 There are exceptions, but it is usually made quite clear when it is meant otherwise.

The other thing to make clear is that the speed of light is not just a constant, but it is also an invariant.
What this means is that, not only does everyone measure the same speed for light, but they get the same answer when they measure the speed of light relative to themselves.

For example, If you are in a spaceship traveling past the earth at 1/2 c and turn on your head light, you will measure the light jumping ahead of you at c. After 1 sec the front of the beam will 300,000 km in front of you, after 2 sec 600,000 km, etc.
For someone on the Earth, your beam will be traveling at c relative to them.  Thus after one sec it will be 300,000 km from the Earth.  But at the same time you will have moved 150,000 km in the same direction, so according to the Earth, after one sec,the front of the beam is only 150,000 km ahead of you. (This gets back to the planet example where the planets don't agree on their relative distances.)

So lets see how this works in an example:
We have the clock 1 light hr from you, that you visually see reading 12:00, and thus conclude reads 1:00
You also have someone passing you on his way to this clock and moving at 0.5 c.   He visually sees the same reading on the Clock (12:00),  however he can't conclude that it is actually 1:00 on that clock at that moment.
He is seeing light that left the clock sometime ago, however, unlike your situation, where the clock has maintained a constant distance for the whole time.   The distance between him and the clock is decreasing.  That means that the light he is seeing now, left that clock when it was further than it is now and further than 1 light hr away.  This also means that the light had to have left the clock more than 1 hr ago, and that it has been ticking for more than 1 hr since the light left it.   If he visually sees the clock as reading 12:00 and knows that the light carrying that info left more than an hr ago, he also knows that the clock reads later than 1:00 "now". (The actual value depends on factors I haven't gone into here.)
Thus we have two observers each seeing exactly the same light coming from the same clock and coming to different answers as to what time it actually is for that clock.

This is known as the "relativity of simultaneity".  It is a fundamental idea in Relativity. (BTW, since the Theory relies so much on the Invariant speed of c, Einstein preferred " The Theory of Invariance" , but even the originators of ideas don't always get to decide what they will eventually be called.)