Mathematical Conundrum

[NQLD_Newby]

Sorry Steven, I posted my last post without realising you had posted some answers. I will take some time to absorb your comments, and come back with further questions.

Thanks for your help by the way.

[Ian Robinson]

Essentially time contracts as the relativitistic object's tau value approaches 0, time will move very much slower cf that of stationary observer's time.

Whole chapters are written on this high school and uni textbooks.

[Sionnagh (Mick)]

As Ian has said, whole chapters have been written on relativity.

Originally Posted by NQLD_Newby

Hi Mick,

Once again please feel free to correct me if I am missing something, but the speed of light is always the speed of light, regardless of your speed. Meaning the speed of light doesn't add itself to your own speed. If you were moving at 100km/hr and turn your lights on, the light coming from your car isn't C+100km/hr it is still C. Therefore if you are moving at the speed of light, you wouldn't see any light at all because it cannot get out in front of you because you are moving at the same speed.

Yes, measurement of the speed of light returns the speed of light irrespective of your speed. If you were stationary and measured the speed of light (from your headlights for example) you would find it moves at, well, the speed of light as expected. If you were travelling at 0.5c (half the speed of light) you would measure the speed of the light to be the speed of light not 0.5c as the difference between the speed of light and your speed. At the same time a stationary observer who also measures the speed of the light that you've just measured would also find it to be moving at the speed of light, not at 1.5c as the sum of your speed and the speed you've recorded for the light.

In fact to be perfectly correct, in the scenario described in the above posts, the observers wouldn't see your lights come on at all, because you and the light from your headlights would arrive at exactly the same time.......I think?

The observers would see the light at the same time as they see you.

In their reference frame they see (for want of a better word) you approaching at the speed of light and the light approaching at the speed of light. In your reference frame you see the light moving away from you at the speed of light and the observer approaching at the speed of light.
What the Lorentz transformation does is give you the relative velocities as seen by different observers. Since the relative velocity of two objects can't exceed the speed of light this doesn't agree with the commonsense explanation from everyday experience and this is what causes the headaches trying to work out what's going on.


Mick

[GrahamL]

this is what causes the headaches trying to work out what's going on.

thats true Mick I get plenty of questions as well as answers reading this

great read btw .. and hi sophie

regards graham

[AGarvin]

As far as the OP goes with the question -

So what exactly is the answer to this equation? What's the time difference between and observer's time and a photon's time?

The answer is it's undefined. You'll more likely hear a physicist say something like it's meaningless to talk about a photons frame of reference since you can't perform a transformation to that frame. Their answer will be more along the lines of the dilation factor tends to infinity as v approaches c.

Andrew.

[Shnoz (Sophie)]

If I may post yet another brain-bending question. Given that nothing in the Universe can exceed the speed of light, would it be possible to calculate an absolute size to our entire Universe?
I would imagine that very simply put it would require a multiplication by the age of the Universe and the speed of light. Of course, things such as the Hubble Constant would have to be taken into account; but to find the biggest size our Universe could possibly be, would such an equation work?

And hello Graham

[xelasnave]

Originally Posted by Shnoz

If I may post yet another brain-bending question. Given that nothing in the Universe can exceed the speed of light, would it be possible to calculate an absolute size to our entire Universe?
I would imagine that very simply put it would require a multiplication by the age of the Universe and the speed of light. Of course, things such as the Hubble Constant would have to be taken into account; but to find the biggest size our Universe could possibly be, would such an equation work?

And hello Graham

I think if you work on the basis of C radiating from a point (the big bang point of which there was none for some there was one for others) you will get a diameter of 26 billion lights years ...however there is more to it than that because space was expanding and it was/is apparently not limited to c speed of light...so it is now 160 billion light years across (apparently how this is arrived at I do not know)...for mine the universe is infinite but what I state is the way I think big bang approaches the matter.

The inflation theory (which is an idea not a theory which irrespective of explaining the flatness or whatever of the universe is given a time frame of 30 or so seconds...all we know in 30 seconds..unbelievable really...so I dont)

anyway inflation suggests a doubling over and over of space such that all we believe to be there (some say 160 billion light years wide ruffly speaking cause its too simple to say it that way ...) was in place in some 30 seconds...now that beats C hands down...anyways someone will expand upon that I feel but one has to think space expansion as unrelated to C as maximum..well it is but space can expand faster than light can travell...and you are right it sounds a little suspect that approach but others may expand here

I mean 30 seconds just think that thru...I dont care what the sums say that does not add up...



alex

[sjastro]

Originally Posted by Shnoz

If I may post yet another brain-bending question. Given that nothing in the Universe can exceed the speed of light, would it be possible to calculate an absolute size to our entire Universe?
I would imagine that very simply put it would require a multiplication by the age of the Universe and the speed of light. Of course, things such as the Hubble Constant would have to be taken into account; but to find the biggest size our Universe could possibly be, would such an equation work?

Sophie,

Nothing can exceed the speed of light through space, but the expansion of space-time can exceed the speed of light. This doesn't contradict special relativity as distance and time in space time expansion is not the same as our customary definition of these terms.

Getting back to your question, multiplying the speed of light by the age of the universe will only give a very rough value of the size of the observable universe. For example during the flight of a 13 billion year old photon, the Universe would have expanded by a certain amount and this needs to be factored in. Unfortunately since the expansion of the Universe is accelerating we only have a snapshot of the Hubble "constant" as it is now, not over the 13 billion year history.

Hence the size of the Universe will always be at best an estimate.

Steven

[Shnoz (Sophie)]

Thanks for explaining. I knew things couldn't be so simple.
But if the universe expands, it doesn't create any new material at its 'edges', it justs stretches everything further and further apart, which is why we see most galaxies moving away from us. At the moment we see them moving away at approximately 70 (km/s)/Mpc.
But universal expansion has been very fast before. During the inflationary period the universe expanded to something close to its size today in less than a minute. But most of the matter was still relatively evenly spread. Would this require the matter to exceed the speed of light, or is there something I am unaware of?

[sjastro]

Originally Posted by Shnoz

Thanks for explaining. I knew things couldn't be so simple.
But if the universe expands, it doesn't create any new material at its 'edges', it justs stretches everything further and further apart, which is why we see most galaxies moving away from us. At the moment we see them moving away at approximately 70 (km/s)/Mpc.
But universal expansion has been very fast before. During the inflationary period the universe expanded to something close to its size today in less than a minute. But most of the matter was still relatively evenly spread. Would this require the matter to exceed the speed of light, or is there something I am unaware of?

The inflationary period lasted from around 10^-36 second to 10^-32 second after the Big Bang. In this period the Universe expanded from 10^-24 cm diameter to about the size of a grapefruit.

There was no matter in the Universe at this stage. If there was no inflationary period the Universe would have collapsed onto itself once matter began to form later on.

Regards

Steven

[Shnoz (Sophie)]

Oh, ok, now I get it. Thanks for sorting that out.

[xelasnave]

Originally Posted by Shnoz

Thanks for explaining. I knew things couldn't be so simple.
But if the universe expands, it doesn't create any new material at its 'edges', it justs stretches everything further and further apart, which is why we see most galaxies moving away from us. At the moment we see them moving away at approximately 70 (km/s)/Mpc.
But universal expansion has been very fast before. During the inflationary period the universe expanded to something close to its size today in less than a minute. But most of the matter was still relatively evenly spread. Would this require the matter to exceed the speed of light, or is there something I am unaware of?

It is space (time) expanding at the dizzy rate but the speed limit within space is c I think...I often wonder what that first packet of energy that left first and is at the very edge..ahead of the rest of the universe that follows into what doth travel... into?... what is on the other side of everything

alex

[bojan]

Originally Posted by xelasnave

what is on the other side of everything

alex

Nothing.

[xelasnave]

Originally Posted by bojan

Nothing.

And what is on the other side of that?


alex

[Shnoz (Sophie)]

I suppose we can only theorise as to what is outside our universe at this point in time. Perhaps it is something that mathematically equates to zero. Or maybe our universe really is something like the locker of another larger universe (forgive my reference to the MIB movie).

[xelasnave]

I doubt if we shall ever know ...that will not prevent us from thinking we know...but speculating is fun.

alex

[sjastro]

Originally Posted by Shnoz

I suppose we can only theorise as to what is outside our universe at this point in time. Perhaps it is something that mathematically equates to zero. Or maybe our universe really is something like the locker of another larger universe (forgive my reference to the MIB movie).

You might find this thread useful.
http://www.iceinspace.com.au/forum/s...988#post359988

Regards

Steven