Jump to content

Light speed questions!


sgazer

Recommended Posts

I've been watching some of Hawking's Universe programmes on Sky, which were very interesting, but they've raised a few questions in my head!

Now, regarding light speed; as an object approaches light speed, time slows down for that object. Hawking usefully described it as a protection for the light speed limit. eg. on a train travelling at near the speed of light, if a person ran forward, they could break the light speed limit, but as time slows down for them, they would not be able to run forward fast enough to break it, in fact, at the speed of light, they would freeze, so they would not be able to move forward at all, thus protecting the speed of light limit.

ok, now suppose we built a very fast space ship capable of travelling very close to the speed of light, so for every minute on the ship, a year passed on earth for example or a ship that can travel at the speed of light. This raises a few questions;

1) when we say it takes 20 light years to get somewhere at the speed of light, is that 20 light years for an observer or 20 light years for the object travelling at the speed of light? I strongly suspect the former, because 20 years at the speed of light would be an infinite time elsewhere as for the object travelling at the speed of light, time would stand still.

2) So close to the speed of light say it takes the space ship 21 earth years to travel 20 light years in space. Time on the ship would travel slowly. If it was 1 minute for every year on earth, then the ship would travel the distance in just 21 minutes from the point of view of the people on the ship (21 years for people on earth).

So assuming this is the case, then as long as we can travel close to the speed of light, it doesn't matter how many light years away a distant star or galaxy is, it could be thousands of light years, but only hours might pass for the people on the "near light speed" ship.

3) however this does throw up another problem, imagine travelling near the speed of light, with time aboard the ship slowed to nearly a standstill. It would take ages for the pilot to move to reach the steering wheel to make a course adjustment! Or even for a preprogrammed computer course adjustment (even that would slow down!). We couldn't operate it remotely from earth as the signal transmitted (at light speed), would take ages to catch up with the ship!

I'm sure there are many other problems with travelling near the speed of light, but these are just a few I came up with :). Anyone got any answers?

oh yes, another one about light itself;

I understand light is basically photons (correct me if I am wrong), I know that something travels through space very quickly then hits my eye or ccd where it can be detected and measured. As light travels at light speed, I presume that zero time has passed for these photons since they were emitted from their source, so they arrive at my eye and ccd exactly as they were when they were emitted. Nothing spectacular, but interesting to think about.

Link to comment
Share on other sites

  • Replies 30
  • Created
  • Last Reply

"Now, regarding light speed; as an object approaches light speed, time slows down for that object. Hawking usefully described it as a protection for the light speed limit. eg. on a train travelling at near the speed of light, if a person ran forward, they could break the light speed limit, but as time slows down for them, they would not be able to run forward fast enough to break it, in fact, at the speed of light, they would freeze, so they would not be able to move forward at all, thus protecting the speed of light limit."

With regard to the above, surely thats relativity and not speed preservation, i.e. the speed of the train to an outside observer is the train going nearly the speed of light, however the speed of the human inside is relative not to an outside observer but only those inside the train. So the human will only be ever, relativly speaking, be going about 15mph max.

Its where relativity gets its name from, if you throw a ball in the air on a train then inside observers will only see vertical movement. An outside observer will see the ball move in both vertical and lateral positions, depending on the speed of the train and the height of the throw, then the outside observer may see it go vertical for 1 metre and lateral for 40 metre's. You can't really say the ball travelled 40 metre's laterally on the train because it never happened.

You can also take energy into this equation, imagine the amount of energy needed to throw the ball in the train laterally over that 40 metre's, its a lot more than throwing it vertically for 1 metre. An outside observer would probably then see the ball travel 1 metre vertically and 80 metres laterally. This is therefore not a true indicator of energy and the energy usage can only be taken from within the train. So relativity is seperate depending on the medium in which its being used.

Wow, thats the most physics I have done on this forum in ages! It's probably all wrong aswell.

Link to comment
Share on other sites

There is always another thing to take in to consideration.

We don't really know as we cant technically prove it.

All we can do is theorise afaik we have been unable to get particles up to the speed of light in accelerators.

As we understand more the more we realise we don't know :)

Link to comment
Share on other sites

We don't really know as we cant technically prove it.

All we can do is theorise afaik we have been unable to get particles up to the speed of light in accelerators.

The Michelson-Morley experiment is a very good proof of special relativity.

We can't accelerate anything to the speed of light (this would take an infinite amount of energy) but we can create photons which must travel at the speed of light. In fact you're doing it right now, you're emitting a huge number of photons in the long infra red / microwave region of the spectrum by virtue of your body temperature.

Link to comment
Share on other sites

Now, regarding light speed; as an object approaches light speed, time slows down for that object.

No, time passes more slowly for the moving object as measured by a stationary observer (relative to it). For example, if a radioactive particle falls to Earth at close to light speed, its time until decay is found to be a lot longer than if it were stationary in a laboratory. But from the particle's point of view it's the Earth that's moving while it remains stationary - so the particle "sees" time on Earth runnnig slower, while its own lifetime feels perfectly normal. This sounds like a contradiction but isn't - Einstein took care of it in 1905.

1) when we say it takes 20 light years to get somewhere at the speed of light, is that 20 light years for an observer or 20 light years for the object travelling at the speed of light? I strongly suspect the former, because 20 years at the speed of light would be an infinite time elsewhere as for the object travelling at the speed of light, time would stand still.

It's 20 years as measured by an observer who is effectively stationary with respect to traveller (i.e. someone on Earth).

then as long as we can travel close to the speed of light, it doesn't matter how many light years away a distant star or galaxy is, it could be thousands of light years, but only hours might pass for the people on the "near light speed" ship.

Correct.

3) however this does throw up another problem, imagine travelling near the speed of light, with time aboard the ship slowed to nearly a standstill. It would take ages for the pilot to move to reach the steering wheel to make a course adjustment!

Yes, as measured by people on Earth. There are subtleties here that we needn't worry about, but suppose you were watching a video feed from the space-ship. You would see everything happening very slowly on board while it whizzes through space. But the people in the space-ship would feel perfectly normal: it's Earth that would be in slow motion. (The subtleties are to do with the fact that the time for signals to travel between Earth and the space-ship keeps changing - this also applies to light seen by the space-ship pilot, whose view in fact turns out to be a small dot right in front of him. So course adjustments aren't really going to be feasible anyway, leaving aside the amount of energy needed to change course when you're moving so fast. We'd need to think of the space-ship as following a geodesic path, effectively "falling" in the background gravitational field).

I understand light is basically photons (correct me if I am wrong), I know that something travels through space very quickly then hits my eye or ccd where it can be detected and measured. As light travels at light speed, I presume that zero time has passed for these photons since they were emitted from their source, so they arrive at my eye and ccd exactly as they were when they were emitted. Nothing spectacular, but interesting to think about.

Yes, effectively no time passes for them. Whether the light reaching your eye is the "same" one that was emitted is another question, discussed here:

http://stargazerslounge.com/physics-space-science-theories/104098-do-we-observe-orignial-photon.html

Link to comment
Share on other sites

With regard to the above, surely thats relativity and not speed preservation, i.e. the speed of the train to an outside observer is the train going nearly the speed of light, however the speed of the human inside is relative not to an outside observer but only those inside the train. So the human will only be ever, relativly speaking, be going about 15mph max.

hmm, that's the sort of thing that makes my head ache! Yes, I think the people moving around in the train won't realise they are moving slowly, they'll just be moving normally compared to everything else on the train, but as they look out of the window I think everything would be aging quicker than they are. Now for an external observer looking in, I presume everything will be aging/moving more slowly.

I don't know, I think I haven't really addressed relativity.....now where's the paracetamol!!

Link to comment
Share on other sites

It's all perfectly simple, really.

The faster you go, the quicker you get there, without limit.

A photon manages to cross the entire universe in no time at all.

Other particles, that have mass, can approach that trick by moving ever closer to the speed of light.

Link to comment
Share on other sites

All objects have a certain speed relative to everything else - Galileo knew that. Newton thought there had to be an absolute "correct" speed relative to space itself, Leibniz thought otherwise and Einstein proved him right. But additionally, Einstein showed that relative speeds don't add together in the simple way that people thought. If you have two spaceships flying head on towards each other at close to the speed of light, both will see the other as travelling at less than light speed, contrary to what we'd normally expect. This is all because of the basic postulate of special relativity, which is that people always measure light to have the same speed - as born out by the Michelson-Morley experiment and countless others.

So the universe is made of two kinds of thing: radiation, which always travels at the speed of light; and matter, which is always measured to travel at less than the speed of light.

(Okay, bring on the tachyons and pass the paracetomols...)

Link to comment
Share on other sites

A photon manages to cross the entire universe in no time at all.

?

A photon would take 13.7 billion years to travel the visible universe according to modern astronomical calculations.

To cross the universe would never happen as there is no defined 'edge' to the universe.

The expansion of space itself would limit any photons from ever reaching the exact limits of the universe...raising the question is the expansion faster than light speed, or did it just have a head start!?

Link to comment
Share on other sites

A photon would take 13.7 billion years to travel the visible universe according to modern astronomical calculations.

These years are timed by a clock that is "co-moving", ie, stationary with respect to the local galaxies.

As you race towards something, Lorentz contraction sets in. This reduces the apparent distance you have to cover. If you go at 99.99999999995% of the speed of light, the reducing factor is 1 million, and there's no limit to how big you can make that factor.

In the limit, as the speed of light is reached, all astronomical distances get Lorentz contracted to 0 and you can cross the universe in no time at all.

Of course, other clocks will show different times but who cares?

Link to comment
Share on other sites

Has anyone ever wondered about the following from Einstein's initial work on special relativity.

If an object moves at velocity v towards a photon travelling at c we would expect the photon's relative velocity to be equal to c + v. Special relativity states that the velocity of the photon would still be c so in this case it must be that the distance between the object and the photon contracts and time dilates so from the point of view of the object the photon's velocity remains unchanged.

However if the object were to head away from the photon then we would expect the velocity to be c - v but special relativity states that the photon should be travelling at c once again in the object's frame of reference.

So if in both cases length contracts and time dilates how can a positive change in velocity in the one case and a negative change in velocity in the other case be cancelled out?

Link to comment
Share on other sites

However if the object were to head away from the photon

What do you mean by this? Nothing can out-run a photon, so the only way you can "head away" from a photon is if it is heading away from you, i.e. in your reference frame you are stationary and there is a light shining away from you.

Link to comment
Share on other sites

OK, so in my rest-frame I see a light source heading away from me with velocity v and photons coming towards me with speed c. What the source sees, in its rest frame, is me flying away from it with velocity v, and photons reaching me with velocity c.

What both of us see is a foreshortening and time dilation of the other. To me, the lamp is squashed and slowed down (i.e. its light is red-shifted). To the lamp, I'm squashed (in the direction of travel), and the light I'm reflecting back to the source is red-shifted.

The effects are of course too small to notice unless v is close to c.

Link to comment
Share on other sites

You need to make a careful diagram of the spacetime events in each coordinate frame. Don't forget to take into account that what is simultaneous in one frame is not in another.

I guess the problem here is that I am not trying to consider relative coordinate frames. The only coordinate frame considered is that of the moving object.

I suppose I just instinctively have trouble grasping the concept that light can be the same speed relative to the object whether the object is heading towards the light source or away from it.

Does special relativity mean to imply that space and time warp for the observer in what ever way is convenient to maintain the constancy of light? :)

Link to comment
Share on other sites

Does special relativity mean to imply that space and time warp for the observer in what ever way is convenient to maintain the constancy of light? :)

Yes, exactly. Though a relativist might say "necessary" rather than "convenient".

Link to comment
Share on other sites

But how is it that space knows to warp one way when the observer is heading away from the source and a different way when the observer is heading towards the source. Wouldn't it need to warp differently in each case to maintain a constant speed of light.

That is the crux of my original question.

Thanks,

G

Link to comment
Share on other sites

There is no absolute space. Observers can measure the same object (or region of space) having different lengths. There is no "right" answer, though the distance you would measure if you were standing still with the object is a convenient standard.

Link to comment
Share on other sites

I think I see but I remain unconvinced :D I guess special relativity is just working out what would need to happen to allow for a constant speed of light, not explaining why there is a constant speed of light so within the theory the answer to my question is as follows.

Say at time zero in the object's frame it could either head towards the light source or away from it with an instantaneous speed V (velocity -v in the first case and velocity v in the second).

The light source has switched on sometime in the past and the first photon of light is on its way to the object at velocity c.

If the object were to measure the passage of time until the photon reaches it in each case the object would measure the same time period t.

This is because in both cases the object's relative velocity is zero in its own frame and the speed of light in both cases is the same.

I can accept it but I don't have to like it :)

Thanks for the help.

Link to comment
Share on other sites

1st case: object A is moving to the right with speed v, photon moving to left with speed c: composing the two velocities, we find that object A is seeing a photon at speed:

(v+c)/(1+ (v*c/c²)) = (v+c)/(1+v/c) = c*(1+v/c)/(1+v/c) = c

2nd case: object A is moving to the left with speed v, photon moving to left with speed c: composing the two velocities, we find that object A is seeing a photon at speed:

(-v+c)/(1-(v*c/c²)) = (c-v)/(1-v/c) = c*(1-v/c)/(1-v/c) = c

more details:

Relativistic Velocities

Link to comment
Share on other sites

I suppose I just instinctively have trouble grasping the concept that light can be the same speed relative to the object whether the object is heading towards the light source or away from it.

Does special relativity mean to imply that space and time warp for the observer in what ever way is convenient to maintain the constancy of light? :)

Not quite. Here's a parable: There is a civilisation whose cities, Athens, Berlin and Calcutta are on huge inclined plane conveniently placed so that North (marked by a Polaris star) points straight uphill. They measure uphill distances towards the North (always using the star) in meridimiles and "flat" distances in equstadia. They never think that these lengths can be exchanged for one another because flat and uphill are very different for all practical purposes, hence the different units. From Athens to Berlin it's 300 equstadia east and 200 meridimiles north. From Athens to Calcutta it's 100 equstadia east and 1200 meridimiles north. From Berlin to Calcutta it's 200 equstadia west and 1000 meridimiles north.

After about a century, a bored young man measures the distances again and finds them

A->B : 300.1288 east (was 300), 95.2551 north (was 200)

A->C : 101.0319 east (was 100), 1164.912 north (was 1200)

Fear, uncertainty and doubt ensue. What's going on? Is the earth moving the cities around? Is the Universe warping? Are the old measures unstable?

Or has Polaris shifted by one degree to the left so that it's no longer pointing straight uphill? The new measurements are then done in a rotated cartesian frame. This mixes the separate units together and for the first time it becomes necessary to establish a conversion ratio between the two. This makes it possible to speak of a distance between cities as one number.

In the old units, this single A-B distance was sqrt(300*300+200*200/(20*20)) = 300.1666

In the new units, A-B is

sqrt(300.1288*300.1288+95.2551*95.2551/(20*20)) = 300.166

With the conversion ratio 20 equstadia to 1 meridimile, all city distances remain the same (try it for A-C, it should give 116.619). The civilisation has unified the flat direction with the uphill direction, the unification of space.

Special relativity has done pretty much the same thing with time and space. Instead of rotations, the different views correspond to different observer velocities. Instead of always summing squares (like in Pythagoras), the squares of time intervals must be subtracted from the squares of space intervals. It is natural to measure space and time in the same units so that they can be mixed without conversion factors in the formulas.

So, would you say, that "flat" and "uphill" have warped for the surveyor in what ever way is convenient to maintain the constancy of city distances? Or would you say that "flat" and "uphill" have been revealed to be only snapshots of the underlying reality?

Link to comment
Share on other sites

wow, it's started quite a debate with some very interesting answers. Thanks for your responses.

The thing that most interests me is (if it's really true) that time slows down for a person travelling close to the speed of light, therefore it doesn't feel like such a long time to them to travel a certain distance. I've always felt constrained by lightspeed and the fact that it would take ages to get anywhere and we must be able to travel faster than light to do so, however 100 light years might not be too bad afterall at near the speed of light as it wouldn't feel like that long. Not that I'll ever find out!

Link to comment
Share on other sites

Archived

This topic is now archived and is closed to further replies.

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...

Important Information

We have placed cookies on your device to help make this website better. You can adjust your cookie settings, otherwise we'll assume you're okay to continue. By using this site, you agree to our Terms of Use.