This is the concept. I’m convinced there’s a better example to illustrate this point and I found one here. Scroll down to the section on time dilation.
Note that we’re talking about time intervals. Einstein isn’t saying cause and effect are violated.
Thanks breaknrun - that is a good site. The mathematics of time dilation due to the constancy of the speed of light are clearer now. However, my real problem is with the claim that simultaneity is not absolute.
Please bear with me, I know anyone who knows the subject inside out must be thinking I’m some kind of freaking idiot. That’s what I get for trying to educate myself… 
I first read the book by brushing over stuff I didn’t get, assuming it would all come out in the wash. Now I’m re-reading, trying to understand the basics, as it turns out that the whole thing hinges on the basics. Don’t get your knickers in a twist; I am assuming that I’m missing something very obvious, not that Albie was a monkey. But I’m sure you can see that unless I get the basics, the rest of the theory jars a bit.
Perhaps the example given in the book is a bad one. The section contains other small errors - maybe they are mistakes in my edition, or maybe Einstein was rushing this section on a Friday afternoon just before rushing out to get lairy on the town with Planck.
About the constancy of the speed of light in all frames of reference:
I know that the book assumes zero knowledge of it’s theory - but Einstein has already laid down earlier in this book the fact that light always travels at a constant speed relative to any observer. In fact, the section in question is meant to be setting up the explanation for why this property of light is possible. The section can be summarised as:
“How can two observers with different reference frames measure the speed of light to be the same? Well, we can show using the train example that simultaneity, and hence time, is different for different observers. Also, we cannot be sure that distance is an absolute either. Thus, the speed of light can appear to be constant in all reference frames.”
But this to me seems to be crazy circular reasoning: “Speed of light is constant. Let’s pretend it isn’t, and - oh! - it not being constant shows that it can be!”.
The pulse source is neither stationary nor moving wrt any FoR - it is a point source of light. For all observers, no matter how they are moving, the light will travel from these points at the same speed in their FoR.
Can you explain please? Perhaps this is my problem.
As I see it, in reality, the observer on the train will see the flashes simultaneously. Where is this idea coming from that he won’t? The light starts equidistant from M, and our observer is moving through M at a constant velocity at the time of the strikes. If he saw one strike before the other, then it means that in his frame of reference the light from B is moving quicker than the light from A.
The Michelson-Morley experiment showed that the velocity of light was constant regardless of motion. I can accept that removing the assumption of time as being absolute explains this neatly.
I can accept time dilation. However, I cannot on the evidence given accept that simultaneity depends on a frame of reference. And, in this case, then space dilation (or the fact that distance has no absolute value) also cannot be accepted, since it in turn is derived from the conclusion above.
There’s no circular reasoning here. He shows that time is relative to the frame of reference. The speed of light was measured to be the same. We don’t know about the absoluteness of distance. But the speed of light CAN APPEAR to be constant in all reference frames. He never “let’s presume” it isn’t.
OK, Sirjamesp, one at a time (hope this is enlightening):
Well, it can seem like there is sort of circular reasoning on Al’s part. It’s not really circular reasoning, though, because he’s not proving anything. He’s just starting with an assumption (speed of light is constant to all observers) and then seeing what the implications of that assumption are. When he reaches a conflict between constant c and other assumptions --like invariant time and space for all observers – then he throws out the assumptions that aren’t constant c. So his argument is really: ‘if the speed of light is constant, then simultaneaity isn’t constant’.
Well, once you look at how the universe really is, it turns out that the speed of light is indeed constant for all observers, and all these funky things like time and space dilation do happen. So he’s right, but most explanations of relativity just start with the constant speed of light as an assumption.
Now, back to the train example. What I was trying to show was that if the train observer sees both flashes at the same time you have a contradiction about which color hanky he raises. This is clearly not possible.
So one of our assumptions is wrong – and IF constant c is right, THEN R can’t see both flashes at the same time.
It’s a really difficult concept to wrap your head around, because of the perfectly logical reasoning that from his point of view both flashes travel the same distance and both went off at the same time. The answer is that, to him, they didn’t go off at the same time.
This is how you get to the whole space contraction thing: (warning! highly compressed explanation!) if R doesn’t see both flashes at once, then he must observe both ends of the train at A and B at the same time, which means to him, the train is a different length than AtoB on the embankment. Remember, we’re just seeing what happens if c is constant, and figuring out what that would mean. Turns out it means when you’re moving past something, it seems shorter to you.
Wow, who’d a thunk it?
I guess it did take an Einstein to figure that out.
Does that help sirjamesp?
I hope you guys don’t mind someone else jumping in…
sirjamesp: I think I may see the problem. It looks to me that you are confusing the “constant speed of light” theory and the “nothing can go faster than light” theory into something to the effect of “light moves infinitely fast.” As Al has pointed out at this point in the text, light moves at a constant, finite speed. This means that although it is quick it will take time to get where it’s going. So as the light from B is rushing toward the train man, the train man is moving toward B and decreasing the distance that the light from B needs to cross to get to him. In the same way, the light from A now has to travel a little farther to get to him. That means that it will take a little less time for the train man to see B and more time to see A compared to the stationary observer. It is not increased speed that causes the effect, but decreased distance.
(1) A* R *B
(2) A** R **B
(3) A*** R ***B
(4) A**** !***B (! = light hitting R)
These diagrams are from the stationary observer’s point of view, by the way. Since the speed of light is constant in all frames, though, it is accurate to explain R’s observations. See how far the light from A still has to go by the time R sees B?
The problem with this example is Al’s combination of everyday objects and experiences (trains, etc.) with concepts like measuring the time difference between lightning strikes. These are “thought experiments” in the sense that you can’t really perform them. Maybe if he used bullets or sprinters (or anything with a speed closer to that of the train) instead of light coming from a source it would be less confusing. The point he is trying to make is that the two observers will not agree whether the strikes were simultaneous or not and that one frame of reference is not inherently “better” than another. You seem to be taking the side of the stationary observer and I think that is because everybody naturally measures things relative to the earth. You associate it with “reality” (see quote above). Again, that’s another flaw in this thought experiment. Perhaps if it were set in space or some place with two “mentally neutral” frames of reference it would be better.
My take (IANAP):
sirjamesp wrote:
okay so far.
Nope. How do you figure they travel the same distance relative to him? (perhaps the concept of relative distance hasn’t been covered yet in the book.) Light travels at a constant speed, but distances are not identical in different reference frames. This is the Lorentz transformation, as Einstein described in general relativity. In the train’s reference frame, the distance to A is contracted, so reaches the observer at M’ sooner than the flash at B, which in the M’ reference frame is farther away than is A.
Ok,
- the Lorentz transformation is central to special relativity also…
- it isn’t need to understand this scenario at all.
Lets point out a couple of thing Einstein assumed was self evident in this example and see if it gets the orginal posters on track. BTW, this idea of simultanity is independent and can stand alone. You can understand this in a vacuum as it were.
- Mark the front edge of the train as position A. I mean the very exact front edge.
- Mark the back edge of the train as position B.
- The observer at the middle of train has measured his position on the train to be EXACTLY between A and B. Call his position M.
- An observer is on the ground beside the track, call his position P.
- As the train sail by position P, there will be a moment whe P and M are side by side. Right at the very moment, lightning will strike A and B, lets let it actually hit the spots on the train.
It is getting ready to get interesting.
-
Here is a list of everything I can think of that both M and P will agree and disagree on.
a) Both will agree the lightning hit spots A and B
b) Both will agree that when each observer sees the lightning that points P and M are NOT side by side. This is very important. Since light has a FINITE speed, P and M are NO LONGER SIDE BY SIDE when the light gets to their vicinity. M will have moved forward (at least a little) during the transit time.
c) Both will agree that M is in the middle of the train between A and B.
d) They will disagree that the lightning struck at the same time. M will deny it, he will see A first, because now he is closer to it due to his motion during the transit time of the light. -
It should be obvious in this instance what the problem is to both observers. The will know the finite speed of light and both will agree M is not aligned with P when the light got there. It isn’t that mysterious to either.
-
The conclusion though has big implications later on. But at this point, it should be obvious that if people aren’t in the same circumstances (frame of reference), they won’t necessarily agree on simultanity. No big deal yet. This isn’t even surprising.
-
8 would lead to the conclusion that if M and P measure the speed of light, they would measure it differently in different directions. To the M, light should travel c+trainspeed from A to M and c-trainspeed from B to M. The rub comes now. They will not.
-
When you combine this idea with the fact that both people when measure c in all directions get the same answer, now you have a problem. Something has to give. Absolute time and Absolute distance is what has to give. It takes these two facts together to found special relativity.
Hopefully, that made it more clear.
And just a bit more.
Mich & Mor as well as Lorentz already understood this example before Einstein put in his two cents.
If you did this experient with sound, it would come out exactly the same. However, with sound, you know the medium it travels through (air) and additive and subtractive velocities would work out just fine.
Einstein did go a bit further with this idea. He did say this example points out:
a) Sending signals is our only real way to define simultanity.
b) As shown above, it doesn’t work very well.
c) Might as well just drop the concect of “absolute” simultanity, and just make it a relative concept.
-
“A” has clocks at the front and back of his train.
-
He sends two pulses of light to start these clocks.
-
Both clocks are synchronized in “A’s” frame.
However A is moving with constant velocity in B’s frame
-
B sees A’s light pulses reach the rear clock first because it has a shorter distance to travel.
-
In B’s frame A’s clocks are not synchronized.
I read that popular book by Einstein in my last year of high school. By that time I decided I was a biologist and not a physicist, and I gave up hope of ever really understanding hard-core physics. I did “minor” in math in college, and after I realized I was too stupid to make a living as a mathematician or physicist, I went to medical school…
But I always liked the way Einstein presented his “thought experiments.” It seemed very Aristotelian, if not Platonic.
One thing I could not understand was the idea that the speed of light limits the ability to communicate between two points in space.
So I concocted this “Gedanken” experiment, and presented it to my High School physics teacher.
Imagine a giant pair of scissors, infinitely light of mass and quite long, suspended in space. These scissors are somewhat open and the handles and fulcrum are close to you. The ends of tghe scissors are way out in intergallactic space. The material of the scissors is rigid, yet infinitely light. You push the handles together. Being a solid mechanical body, shouldn’t the ends of the scissors come together according to the Newtonian laws of motion? If so, wouldn’t there be a point at which the ends of the scissors would be moving faster than the speed of light?
Of course I figured that there would be a reason they could not. The obvious answer is that massless scissors cannot exists, and as the velocity of their parts increases, so does their mass and inertia, so that the scissors would “bend” just so much to prevent their faster than light movement. Not to mention that an impossible amount of energy would need to be applied to overcome the inertia.
Nonetheless, the thought experiment seemed intersting to my 15 year-old mind.
I’ve always had a very basic problem with Einstein’s “Special Relativity Theory,” but let me back up for a moment.
Relativity theory obviously states that the speed of an object is relative to the speed, direction, and angle of the observer. This is true in almost all cases. A car going 60mph is passed by a car going 70mph. The driver in the 60mph car measures the other car going away from it at 10mph. An observer on the side of the road sees the cars going 60 and 70.
Makes sense.
But then when we discovered the speed of light, we made the startling discovery that the speed of light is always the same regardless of the speed, direction or angle of the observer. It makes no sense. So Einstein pops up and throws “time” into the equation to explain it.
That bothers me. For one thing we don’t have any evidence that time is an element which can be affected by the laws of physics. My other problem is, instead of stretching for this theory, why didn’t we first question whether or not our measurement of the speed of light is accurate?
If nothing can travel faster than light, then how can we have a device which accurately measures it? Couldn’t such devices be in error by even a fraction of an amount? And if so, that error could account for our inaccurate observation of light always moving the same speed.
If your speedometer only goes up to 120. You’ll never know that your car is actually going 122. And even though you’re passing another car which is really going 120, both your readings measure 120. So Einstein has to pop up and throw time into the equation to explain how you can pass that other car when you’re both going the same speed.
Mr Potts –
Relativity is definitely very bizarre and against common sense. But we do, in fact, have lots and lots of evidence that believe it or not, this is how our universe works.
Al kinds of things have been measured accurately enough to see if they act like relativity says they will, and in every case, indeed relativity gives the right answer.
This is not just measuring speed of light, but also time and space contraction, and lots of effects predicted by the general theory of relativity (which links gravity and acceleration and space-time and we don’t really want to go into right now except to say that it expands on the relativity theory we’re talking about right now).
So maybe Einstein pulled the theory out of his, uh, ear, but every time physicists have checked, it works pretty well for our universe.
Actually, we do have lots of evidence that this is exactly the case. Subatomic particles in particle accelerators exist longer than they do “at rest”, by exactly the amount that relativity predicts. My favorite example from a long list is GPS; the clocks on GPS satellites are set deliberately so they do not keep correct time when sitting on the Earth’s surface, but they do keep correct time when in orbit (moving relative to the Earth’s surface and higher in Earth’s gravity well than the Earth’s surface). That is, GPS would not work unless “time is an element which can be affected by the laws of physics” in exactly the manner predicted by relativity. See What good is fundamental physics to the person on the street? and Project A: Global Positioning System (a PDF document).
Well, to be pedantic, it’s formally meaningless (since 1983) to measure the speed of light; the speed of light is accepted as a fundamental constant, and our units of length are defined by the speed of light (see Unit of length (meter)). However, your question deserves an answer. You do not need to travel faster than the speed of light to measure the speed of light. Many very clever people used lots of very sophisticated equipment to measure the speed of light in vacuum in many independent ways, and (within experimental error) the answer is constant. See A History of the Speed of light.
Just to be picky, it’s not quite true that nothing can travel faster than light. Nothing can be accelerated faster than the speed of light since that would require infinite energy. That doesn’t preclude tachyons, which can travel faster since their speed was faster than the speed of light at creation. However, we can have no direct knowledge or info about them.