OT : Relativity question.

It also shows time dilation. The light pulse will appear to take a longer and longer time to reach the forward mirror each time as the traveler's speed increases as measured by the "rest" frame observer. At the limit of traveling at the speed of light the time taken will approach infinity making time for the traveler appear to slow down and come to a halt.

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Rick C

0.87c wrt the 'stationary' mile markers I set out previously.

Good, thanks, so the speedo /can/ show >c if it's a 'conventional' device.

Cheers

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Syd

The question is not "wrt", it is "WHO" is doing the measuring. If an observer on the mile posts is measuring the speed, time and distance, then you will get different results than if any of these are measured by the traveler. I think you are asking for the speed and distance to be measured by an observer on the mileposts and time is measured by the traveler. That will give you wonky results which seem to bother you.

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Rick C

I don't think displayed speeds of >c are wonky, I just wanted clarification that it was possible. Some people seemed to be saying it wasn't, but without really saying why.

If the mile posts are less than one mile apart as measured by the fast traveller, then I suppose that must mean that the total distance measured by the fast traveller is less than would be measured by a slow traveller? But I don't know how you'd measure the mile posts.

Cheers

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Syd

Bounce a light beam off them and measure the doppler and return time. This is all the same as if you weren't moving, just the numbers will be different.

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Rick C

If you insist on dividing the time as measured in your own frame of reference into the distance measured in the stationary frame of reference then you will get a silly answer. You will have travelled 1.74 light years at 0.87c in one year of your own elapsed time. (I haven't checked the arithmetic)

Much like dividing apples by oranges.

If you understood relativity then you would conclude that you were travelling at 0.87c no matter what inertial reference frame you used to do the actual measurements. That is the essence of special relativity - that the laws of physics are the same for all observers in inertial frames of reference.

Life gets even harder in GR where there a covariant and contravariant tensors that must be distinguished. Common sense really doesn't work at relativistic speeds or strong gravity you have to use the mathematics.

Natural language is just too ambiguous for describing this stuff!

Regards, Martin Brown

I'm not insisting. My spaceship speedometer works that way, just like the one in my car. But why is the answer silly? It's not like some random number, I can use it to calculate _my_ arrival time if I know the distance, for instance. Just because it reads >c doesn't mean it must be ignored.

So, I take it you agree that my 'car type' speedometer can show >c and that it isn't a meaningless number? Seriously, a yes or no would be good here.

Now that would be meaningless.

Cheers

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Syd

Syd, I guess you can do what ever you want. One of the rules of the world that we live in is that c is the fastest you can go... It's basically on a par with energy conservation.

Let me ask you this, say you are going 0.99 c how fast does your speedometer say you are going? And how is that number of any use?

George H.

Your car speedometer works by actually measuring a physical interaction - the rotation of your tires as you head down the road.

A space-ship "speedometer" doesn't have that luxury - there isn't really an interaction with a measurable medium it can work with. Instead, a space-ship "speedometer" can only work by calculating the ratio of two things it can (try to) measure - elapsed distance, and elapsed time.

The reason things get confusing, is that when you're travelling close to C, either one or the other (time or distance) won't measure out in the same way that it will to an observer at rest.

If you were to (e.g.) fly across the entire width of the galaxy (say,

100,000 light years), at very close to C, you might get to the far side after a period that your watch (and quartz-crystal oscillator, and rubidium frequency standard, and etc.) tells you is one year. Since you'd measured the diameter of the galaxy before starting, and programmed it into your "calculating" speedometer, your speedometer might tell you that you'd been traveling at 100,000 times C.

If you stop, turn around, and fly back, you'd see the same thing: your calculating speedometer would claim a speed of 100,000 C. You'd get back home after two years have passed (for you), traveling at what your calculations told you was 100,000 C the whole way. [Turning around at that speed would be a doozie, but let's just decide you did a slingshot around a black hole, OK?].

Now - here's the problem. When you get back home, the clocks at home (assuming there are any left) will claim that 200,000 years have passed since you left. If you adjust your clock to match that of Earth, your speedometer reading will drop to say that you'd been traveling at 0.999999C. If you don't adjust your clock, the speedo will still claim 100,000C, but your idea of the current date won't match that of the remote descendents you might meet on Earth.

To complicate things - when you are flying across the galaxy at extremely high speeds, and you look out the front window, the galaxy won't look like it does if you were "at rest". It will look to you as if it's been "smushed" forwards towards you, and flattened. As you pass stars and planets and solar systems, they'll all appear to be shorter (in the distance of your travel) than you would expect, and thus you'll fly past them more quickly than you had though.

If you look at the geometry and try to figure out how far it actually is to the far side of the galaxy... you'll find that it appears to be less than one light-year away! If you do your "time vs. distance" calculations based on how the galaxy looks when you're traveling this fast, your calculating speedometer will say that you're traveling at

0.9999C!

Your speedometer will thus be dreadfully confused. Its results - nay, the very inputs that it depends upon to do a calculation - will depend on just when you look and how fast you're moving when you do. Both time measurements, and distance measurements, are *relative*, not absolute... they depend on the motion of the party doing the measurement.

Yeah, it's weird.

Yes, I know that, I'm not a nutter with a foil hat. I was just trying to clarify whether or not a /conventional/ speedometer might indicate more than c. And it can, but few people seem able to admit this.

Dunno. Much more than 3E8 m/s, assuming it's 'conventional', by which I mean timing pre-arranged mile markers using my onboard clock. Do you disagree?

Why should it be of use? But the number is not random. I could use it to calculate my arrival time, for example.

Cheers

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Syd

Hmm well to me numbers go into some equation and give me a guesstimate of how "big" to make the next gizmo.

How many muons make it from the upper atmosphere to the Earth's surface, and my detector?

If you are seriously interested in special relativity, go read spacetime physics, taylor and wheeler. Wisdom for ~$5 on abe books.

George H.

Thank you, I understand that. My speedometer can read more than c.

I had thought so, but was starting to doubt my reasoning, mostly due to people who only know what they've been taught telling me I don't understand.

Cheers

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Syd

George. My speedo says I'm doing 3c. I have three light years distance to my destination as indicated in my galactic atlas. Therefore it'll take me a year to get there. How much more useful to you want a number to be?

So do you agree that my 'conventional' speedometer can read >c?

Cheers

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Syd

I agree. If your spaceship were to continually accelerate indefinitely, the speedometer would eventually indicate something greater than c. But if you consider time dialation, your clock is running slow relative to the ground, so your actual speed is less than c. .

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Yes. But only because you are making an invalid assumption that the poles that you so carefully arranged in the rest frame are still 1 mile apart in the moving frame. The distinction you are failing to make is that you have to use measurements all made in the *SAME* inertial frame to get consistent answers. Dividing rest frame distance by moving frame time will give you a non-sensical answer with no useful interpretation.

You clearly don't understand.

Regards, Martin Brown

It's not a random number, and one useful interpretation could be to allow you to work out /my/ remaining journey time. If my 'conventional' speedo reads 3c, and I have 6 light years to go - as scaled off my printed star chart - then it will take me two of my years.

If the above is true, then the indicated speed is not nonsensical and has a useful interpretation. Agree?

Cheers

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Syd

Sorry, typo.

Cheers

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Syd

This analysis is faulty because it is only from the perspective of an observer in the frame of reference of the mileposts. The question is about the perspective of the traveler.

There is no "rest" frame. There are only two frames of reference with motion between them.

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Rick C

What's not to get?

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Rick C