2.27 Times the Speed of Light.. ?

Two astronauts are floating in space side by side. They push off of each other so as to drift away to a point 2 light-seconds (2Ls) apart where they each find a small space craft. They get into their respective crafts and fall asleep.

Suddenly they awake to a crashing sound. They each get out of their ships to discover that somehow they have crashed together. Each, not wanting to admit that he had fallen asleep blames the other of not watching where he was going while claiming that he hadn’t, himself, moved.

To settle the argument, one realizes that his ship has a travel clock installed. So he goes in to read his travel clock and find that it reads that before the crash, 0.88 seconds of travel transpired. He gets out to apologize but then realizes that something must be wrong.

He knows that they were 2Ls apart and that it is impossible to travel faster than light, so they wonder how it could be that he could be measuring that in only 0.88 seconds, they crashed, making his travel speed (2/.88) 2.27 times the speed of light.

They first reason that maybe both traveled. But what would they be traveling with respect to if not merely to each other? They know that there is no such thing as any absolute frame, so they can only realize travel due to the distance measured between them, not being able to claim which really moved or even that they both moved. And as they measured the distance between them and the time taking place wherein that distance went to zero, it is apparent that 2Ls/0.88 secs leaves a speed of 2.27c.

What happened?

[size=150]Special Relativity DOES NOT SOLVE THIS PROBLEM!![/size]

Answer:
.derived are speeds other all which from frame absolute the is, affect speed of maximum the, light, 0 of field gravity a Given

Can you explain that again…? For the thickos…? ie. Me…?

Emm… not without specific questions. I have my own degree of “thickness” and can’t read your mind (very well anyway). 8-[

I did read it backwards, however, it made only barely better sense than it did forwards.

Okay - I get that in the absence of other landmarks the only things they have as points of reference are eachother, and the distance between them, that they seemed to have covered in a paradoxically quick time…

I just didn’t get the answer. Is this one of those “torchbeam flashed around the surface of the moon/motion faster than light” thingummyjiggs…?

The point is that to resolve the problem with physics, you have to introduce an absolute frame of reference wherein something occurs independent of all observers. But in doing so, you run into the special relativity notion that there can be no absolute frame.

It is my understanding that the problem with the scenario is that space elongates for something approaching the speed of light. Because of that, relative to each other they each are effectively pushing away from each other as they are approaching each other. So if you have two objects, each approaching the other at the speed of light, they actually only approach each other at the speed of light, not faster than the speed of light.

So, relative to each other they are still going the speed of light.

What I think you were trying to say is that because they are moving, the distance they move is longer or shorter. But longer or shorter with respect to what?? The theory is that they would experience or measure a different distance while they were at high speed. But we are not talking about what they saw as they traveled. They saw nothing and didn’t even know that they had traveled other than the obvious note that 2Ls of distance that they had already measured vanished in what appeared to be 0.88secs.

If you are going to deduce a length dilation, by what proposition are you going to posit its accuracy? You cannot do it without declaring that there is this OTHER frame that is NOT traveling and thus we have to use that other frame to alter our measurements so our physics formula will be right. What other “non-moving”/“inertial” frame?

What I’m arguing is that if two objects going the speed of light are approaching each other from a distance of 2Ls, it will take 2 seconds for them to reach each other. Otherwise the speed of light would be exceeded. It is my understanding that this is what is actually observed, though if you have a source I’d gladly reconsider my position.

I see what you mean with the frame of reference(I hope) but shouldn’t the fastest it could take them be one second? Or am i just missing this. And is the .88 seconds from the ships frame of reference? because time moves slower for moving objects so in reality could it have actually taken them more than .88 seconds which in turn would explain it. As you can tell, slightly confused over here :-k

That is exactly what is accepted in physics. So what happened? How is it that they measure that it only took 0.88secs?

I’m not sure what you mean by that…? Did you mean that Science has observed the truth of that statement?

I am not disputing your statement. But the scenario in the OP is doable by Science principles… except for that nasty forbidding of an absolute frame. Otherwise, it works well with all know principles of Science.

Why 1 sec?

The reading of 0.88 came from one of the ship’s “travel clock” (running only during travel).

Fine. So how much longer and by what means of measure would you know?

Btw, the typical formula for calculating time (or length) dilation is;

df = 1 / (1-(v/c)[1]2[/size])[2]1/2[/size]

In case you can’t make that out;
dilation factor = 1 divided by the quantity of the square root of (1 minus the square of (sample_velocity divided by the speed of light))


  1. size=50 ↩︎

  2. size=50 ↩︎

Basically there relative speeds may appear to be x from their frame of reference but in fact it is not >c and the rule of composition of velocities applies. Looking at

we can use the lorentz transform thusly

The question is poorly phrased though as it would never be possible to measure a time difference that would give 2.27 times light, but that said basically relativistically speeds approaching c don’t add because of time dilation and space contraction effects.

This “problem” is entirely flawed from the beginning.

First, however, a note. Special relativity doesn’t simply say that there is no absolute reference frame. It assumes that changing the reference frame one uses does not change the fundamentals of physics and that the speed of light is the same in all reference frames. This means that for a large range of reference frames, we can choose whatever we want and we will get the same events happening according to the laws of physics. It also means that there is no absolute reference frame that is picked out by the events in physics; i.e., there is not one special frame where everything works out or where all the laws of physics have their true form.

OK, so now to the problems.

One thing that is a prerequisite to any discussion of physics is a reference frame for measurement. In non relativistic scenarios we can assume a vague reference frame, but in relativistic scenarios we need to understand what reference frame we are using because it matters to the calculations. In this case, we are not told the reference frames in which the “2 light-seconds (2Ls) apart” is given.

In this case, I could presume that both ships are at rest relative to one another and that the distance given is in a reference frame currently at rest with respect to the ships. However, this is information that should be supplied at the start.

We have to know what a “travel clock” is. Does this measure the travel against a given reference frame? The reference frame that should have been given above but wasn’t? And what was the speed relative to the given reference frame? Is it the measurement of how long the engine was firing?

The distance between each ship is not a constant thing, it is something that depends on the reference frame that we use to determine the distance. Through choice of reference frame, we can make the distance between the ships arbitrarily small.

I fear that in the above question there is a confusion between an absolute reference frame and a reference frame as an intellectual artifact. An absolute reference frame is a particular frame that is picked out by peculiar physical laws or phenomena; this is something that is effectively ruled out by special relativity. A reference frame is an intellectual artifact that we use to describe physical situations and always has been; this is something used by special relativity. In order to describe distances and use physics, we need a reference frame.

I am afraid that I simple do not understand what this is supposed to mean.

I’m glad I’m not the only one. Nice expansion Physbang.

Nice explanation.

The question itself is paradoxical though, therein lies the problem, if you understood special relativity you would never ask that particular question in that particular way. you’d maybe say 1.98x the speed of light, but 2.27 would break the laws of physics as we know them in the first place and would be out of kilter with all measurable scientific fact.

Right, what I’m saying is that the 0.88s thing doesn’t happen.

The second postulate of special relativity is: As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.

All entities involved in the example are inertial frames of reference, since two objects traveling at c towards each other are at a constant velocity, and any stationary observer would also be in an inertial frame. So, we are good to go. No violations here. It is that pesky bit in the denominator that normally gets ignored because, well, how often do we calculate velocity for things approaching c? It’s all about Einstein’s flashlight.

Now there is a surprising first statement from you. {{NOT!}}

You are given all of the information necessary to answer the question of what happened. The challenge is to do it without introducing an absolute frame which is by definition independent of the observers.

Exactly correct.

But the 0.88secs does happen. So explain how. :sunglasses:

Source?

Of?