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As originally devised, the theory of relativity rests on the speed of light being a constant, and time being a fourth dimension to be added to the three spatial ones. The origins of these ideas include late nineteenth century experiments to investigate the possible role of a postulated aether in the mechanics of light. The reasoning at the time was that, similar to the manner sound waves are theorized to travel through air, light must travel through something, given that it can travel through what is otherwise considered a vacuum. But to the surprise of the researchers – by virtue of their failed experiment that didn’t find what they were looking for – it seemed their postulated aether did not exist. To be accurate, we should only say that they found no evidence to support its existence, as you can never find an absence.
Despite the experiment’s failure, the results were of some use in theory-building. To some, they proved that light traveled at the same speed in all directions – at least under the experimental conditions involved. This was taken a bit further by others who simply said that light’s velocity was an unchanging constant.
Of course, measuring the movement of anything has to be done relative to something else. For example, if we were in a speeding van, we might ask a dog traveling with us to sit still, meaning that the dog should not run about relative to the van. But we can’t reasonably expect the dog to become still relative to the road below, given that both van and dog are traveling relative to the road. So what the experiment showed might be more fully detailed by saying that the velocity of light is constant in all directions relative to the source of the light.
Intuitively we feel that if something is moving away from us and something else is moving away from that first thing in the same direction, then the second thing is moving away from us faster than the first. So, as regards the velocity of light, common sense would expect that light sent from something already traveling at the speed of light would travel at twice the speed of light. But there are a couple of problems here. Firstly, the basic speed of light – relative to its source – is incredibly fast. We can forget all ideas about directly seeing or measuring light traveling, given that it moves at the speed of light. To measure its velocity, we must rely on our minds to think through various experimental challenges. But this leads to the second problem which is – again because light moves so incredibly fast – that nothing works fast enough to catch just how fast it moves. Nonetheless, it has long been agreed that the basic speed of light – i.e. relative to its source – has been measured through a combination of experimentation and reason – and is therefore known.
The theory of relativity is based on a significantly more concrete position and has different ideas about what happens as velocity increases. The original version of relativity thought that light always travels at the same speed and can never travel faster than that speed, relative to anything at all that we might consider. Typically, illustrations of this principle consider for example, what might happen when a very short burst of light is emitted from the front of a theoretical rocket traveling at the speed of light. Just as mentioned above, common sense makes us want to double the speed of light to get the resultant speed, but relativity refutes this idea. According to relativity, faster and faster is the wrong principle when things are already moving near the speed of light. Relativity says that rather than an accelerating object just continually getting faster through time, time itself actually gets distorted at very high speeds. In fact, many physicists currently believe nothing at all can travel faster than the accepted speed of light.
Given how we normally think about our world, this sort of idea is more than just surprising – it’s positively mind-bending as it also includes other bizarre notions such as that space is somehow curved, and that time travel might be possible. Relativity also says that if you are speeding incredibly fast towards light that is itself speeding towards you, the light will meet you no faster than if you stood still.
An important point to note here is that none of this stuff can be directly seen or demonstrated. It’s mostly theoretical: projections of the human mind based on reworking previous theories alongside some very limited observations. A lot of the theory is in fact based on purely mathematical reasoning that is disconnected from any real-world theories, never mind actual observations.
To get a feel for how relativity thinks, consider how you would handle a situation in which you added two apples to a hundred apples but only got a hundred and one apples. We immediately say this is impossible, but if you were working on a different problem in a purely mathematical situation with complex formulae the impossibility of this might not be so obvious. How would you work out what was happening? There are two obvious approaches to this. One is to say that the principles or the information you are working with must be incorrect – a bit like saying someone must have miscounted and maybe the hundred apples were actually only ninety-nine. The other way to resolve the problem is to say that we must somehow expand our thinking to allow things to be taking place that we do not normally consider possible. As regards the apples, this is maybe like considering, for example, that as you accumulate a lot of apples the odd apple gets hidden away in some other universe and so you lose one.
Of course, relativity is not about counting apples. The problem with verifying certain ideas of relativity first hand is that perception and the brain are just too slow to capture what really happens at incredibly high speeds. So, crazy though relativity might sound, we cannot actually look at anything to directly check whether it is appropriate or not. What actually happens at very high velocities must ultimately remain conjecture. So, is there a fault in relativity theory, or do we really live in an apparently crazy universe? Or have physicists inadvertently made it sound crazy because without experience of traveling remotely near the speed of light no one can truly know what they are talking about?
To make things simpler, we can examine an example of objects moving at slower speeds. Consider a car moving at 50km/s that fires a projectile in front of it at 150km/s. Discounting the slowing effects of air resistance etc., the speed of the projectile, relative to stationary observers is obviously 200km/s. However, the speed of the projectile relative to occupants of the car is still only 150km/s. Unsurprisingly, this seems to contradict any idea that the projectile has a uniform defined velocity for all observers, and this is why the idea that light always travels at a uniform speed for all observers seems unsettling to us. According to relativity, the speed of our light burst can’t just be added to the speed of our rocket letting us conclude that the burst of light is traveling at a velocity twice the accepted speed of light. But why not?
Let’s de-construct this and look for errors in the thinking. When we are working with our slow car-and-projectile model we can obviously discount the negligibly small time taken for light to reach our eyes or whatever recording devices we use to time the trajectories and to subsequently calculate speeds. So, if we take two points along the trajectory, and record the time for the projectile to travel between the two points, this will obviously give us the essentials to calculate speed. Note that the speed thus calculated by a standing observer would now be the same as that of the occupants of the car, or anyone else, and would indeed be 200km/s. The conclusion would no longer be relative to the specific observer and would indicate that the differences between their previous perceptions of different speeds were indeed only relative to their different conditions in terms of movement. Using this second methodology, the speed of the projectile is uniformly 200km/s regardless of an observer’s position or movement. Notably though, there is no fixed speed of the projectile, should we care to repeat the experiment but vary the specifications. Had the projectile been fired, at say 100km/s from a car traveling at 250km/s its speed would have been 350 km/s for all observers in all positions. This is all intuitive common sense and not something the average physicist would dispute. And note that this demonstrates observations of constant speed for all observers of the same moving objects, regardless of observer conditions, whilst not in any way suggesting that all moving objects move at the same velocity. If all this were extrapolated to the speed of light, we would say that the speed of a specific instance of light is constant for all observers, but that different instances of light can travel at different speeds – ultimately all relative to some set positions in space, or a specified frame of reference.
But we know that things are more difficult to investigate when we consider movements at or near the basic speed of light. Specifically, things happen so fast that the time taken for light to travel from any points along a trajectory to any observers can no longer be neglected as insignificant and must be factored in. What will happen when we do another thought experiment analogous to the moving car and projectile, but at much higher speed?
Logically, no key principles should change simply because we speed things up, as that only changes the figures we use. A variation on the car-and-projectile example should not change our common-sense perspective of what’s happening. Or so we think. But relativity steps in at this point and says we need to change the rules. Because relativity refuses to allow speed to increase indefinitely as the slow-moving projectile is effectively able to do, it has to put any would-be extra speed somewhere else, and so it changes the speed of time to allow the would-be extra speed of light to be slowed down by time itself.
Consider an experiment in which a stationary object at X emits a burst of light at the exact moment a rocket passes X at the speed of light and also emits its own burst of light. The rocket is traveling towards Y which is distance D from X, and an observer at Y is ready to decide if he’ll accept the theory of relativity or not. Relativity states both bursts of light will arrive at Y at the same time, whereas common sense says the burst of light from the rocket will be faster and so arrive at Y in advance of the light from the stationary object. It looks as if this experiment should settle matters.
Now let’s consider two scenarios of the light arriving at Y and compare how relativity and common sense would interpret them. Firstly, suppose the observer at Y reports that both bursts of light arrive simultaneously. If we really trust what we have already hypothesized in our thought experiment to be true, it would look as if the situation is decided and relativity has won the debate. However, someone who believes firmly in the conventional perspective could argue that the experiment was rigged and that things are not really as they appear. They could for example, argue that the burst of light from the rocket was actually emitted at distance D before X and so, although it was traveling at twice the speed of the other burst of light, it had twice the distance to cover and so arrived at Y at the same time. Any number of other theoretical cheating ideas could allow for the fact that both bursts of light appear to arrive simultaneously at Y when they were nonetheless traveling at different speeds. What we establish by this thinking is that to remove doubt from the situation we need trustworthy observers everywhere to tell us exactly what happens.
Our second scenario is that one burst of light arrives at Y in advance of the other. But however much the conventional thinker might want to then argue that his theory wins the case, the adherent of relativity is equally entitled to argue that the experiment has been rigged in a different manner, and so, once again, nothing can be settled until we have reliable information about what really happens within a fully monitored experiment leaving no area for doubt.
Next, it is agreed between our two thinkers that a plan should be devised to ensure both bursts of light do indeed leave point X at the same time. However, they cannot agree on the correct plan. The problem is that everything happens so quickly with light that it is obviously impossible to simply use eyes to record what is happening. But at least both thinkers are agreed on the nature of this particular problem which can be summarized by realizing that when we look at light coming from, for example, some distant star, we have absolutely no intuitive means of knowing its velocity and so would not know if it was instantaneous or had taken billions of years to reach our eyes by moving relatively slowly.
A curious side to this problem is that if we did know how fast the light struck our eyes we could calculate an idea of how long it had taken to travel from the star and – assuming we knew the distance between ourselves and the star – work out its speed. But why would we bother to do that if we already knew how fast the light struck our eyes? We wouldn’t. Our reality remains that we cannot know the speed of light from our eyesight – but we can work it out if we know the distance to the star and how long it has taken the light to reach us. But how are we to know the distance between the star and ourselves? We can actually use the speed of light and its time of travel to do this. But aren’t we using the distance to the star in the first place to calculate light speed? Such thinking is obviously circular. And it’s only more worrying that we haven’t yet considered relativity’s idea that the speed of light is inflexible. Even if the star was receding away from us, relativity says the light would still reach us at the same speed. It seems the speed of light and the way it supposedly behaves controls too much of this thinking.
Nonetheless, within modern physics, these worries are largely dismissed. Light travel is recorded using technology that responds incredibly quickly, and using theory and mathematics, the inflexible speed of light has been calculated – or so most physicists believe, even if not everyone is convinced of all the related ideas. Anyway, the next problem our two thinkers face is that they cannot even agree on how to set up their experiment. Exact timing is obviously crucial.
The relativity thinker explains that by using light from a third stationary source at X and bounced back to X using a mirror at Y it is possible to check that everything is measured very accurately by subsequently compensating for the known time delay for light within the setup. This he argues is one element within a sort of perfect clock system providing the required accuracy of measurements plus all compensations essential to a reliable experiment. But the conventional thinker says there is still something funny about using light to manage a system designed to measure the speed of light.
Let’s take up their conversation. The conventional thinker is called Thicko and the relativity thinker is called Dimbo. Thicko doesn’t mind his name as he feels modern physics is mostly over his head and so he thinks with what he calls gut feelings – even though that’s why some people call him thick. Dimbo, on the other hand, is annoyed at his name. He’s the studious type and even though this means most of his ideas have just been learned from others, he doesn’t feel that he should have to waste time explaining established facts to people like Thicko.
Dimbo: Okay, so we are agreed that we need to monitor things fully. Yes?
Thicko: Sure.
Dimbo: You don’t sound totally happy.
Thicko: No. I’m trying to think.
Dimbo: Think about what?
Thicko: Well I’ve realized that that is all we do.
Dimbo: You mean, think?
Thicko: Yeah. It’s a problem.
Dimbo: I know. We have lots of problems. That’s why we’re thinking! To solve them.
Thicko: But that’s another problem.
Dimbo: What is?
Thicko: Thinking to solve problems.
Dimbo: You think we’re going to solve them if we don’t think?
Thicko: No. But it seems sometimes that the more we think, the more problems we create.
Dimbo: You’re thick! We already have some problems and I’m thinking about how to solve them while you’re wasting time thinking that thinking makes more problems. If you think thinking creates more problems, at least stop thinking and make it easy for the rest of us.
Thicko: Sorry, but I think I’ve got another problem.
Dimbo: What?
Thicko: We’re just imaginary people in a big thought experiment.
Dimbo: How did you figure that?
Thicko: I didn’t. It was just a thought.
Dimbo: Okay, okay, okay! You win. It’s not worth an argument. We’re both just imaginary people in a big thought experiment. Have it your way. Now can we get back to sorting out this speed-of-light thing?
Thicko: Okay... sorry, where were we?
Dimbo: I suggested a technical timing system to verify exactly what happens at both X and Y – a sort of light-based clock. But you, unfortunately, were not happy with it.
Thicko: Well what now?
Dimbo: How would I know? If it were a game of chess, I would say it’s your move. Any bright ideas? Any light-bulb moments?
Thicko: Nah. But I have come up with another problem.
Dimbo: I have been known to get violent.
Thicko: Violence never solved anything.
Dimbo: Mmm... Progress comes from questioning accepted ideas.
Thicko: Are you sure about that?
Dimbo: Yes. See! Now you’re questioning my idea.
Thicko: Yes. I’m trying to make some progress.
Dimbo: Mmm... You’d have more success trying to regress!
Thicko: You know that’s impossible. How can anyone regress? You can’t bend time backward.
Dimbo: Let me think about that one. Actually, you’re sort of right! Regression would be uniquely impossible in your particular case... though not for the reason you mention.
Thicko: So, can we continue with the progress?
Dimbo: One wonders... Any suggestions?
Thicko: Yes. Can we get back to my last problem?
Dimbo: Amazing! We both thought it impossible, but you’re successfully regressing.
Thicko: You don’t understand me. I’m responding to your request to make progress.
Dimbo: You don’t believe in ESP by any chance, do you?
Thicko: I might. Why?
Dimbo: Might have known! Crank! Anyway, I just understood your problem without you explaining it.
Thicko: Nonsense! I bet you can’t tell me what it is.
Dimbo: You’re right. But again, not for the reason you think. It seems no one can tell you anything.
Thicko: You really do waste time. Why did you start talking about ESP?
Dimbo: That wasn’t a waste of time. Just the fact that you had to ask that question proves there’s no ESP. Let’s say I ran a successful thought experiment by actually thinking.
Thicko: Oh yeah? Well, let’s say I still think you waste time – if that keeps you happy.
Dimbo: I’m supposed to be happy because you think I waste time?
Thicko: Let’s say that was another successful thought experiment and it just proved you’re wasting time. I mean, didn’t you say you wanted to get back to the speed-of-light thing? As regards that, it’s actually me who wants to progress!
Dimbo: You mean regress, even though you think it is progress.
Thicko: You are mad. I said progress, you tell me I think progress, and yet you say I mean regress. How can anyone have a meaningful conversation with someone like you?
Dimbo: You’re just wasting more time. What’s that question got to do with the speed of light?
Thicko: Everything! I am trying to communicate with you – to ask you how we can make progress on the matter if we regress?
Dimbo: Don’t you know that light travels out at the same velocity in all directions from a fixed source? Now apply that idea elsewhere.
Thicko: You mean progress and regress are the same things?
Dimbo: Sort of.
Thicko: Well it’s funny you should say that because if you want to regress back a few hundred years, I think you’ll find no one was talking all this relativity nonsense.
Dimbo: You’re even better than I imagined at regressing! Maybe those wackos who believe we humans roamed the planet among the dinosaurs had something after all. Hmmm...
Thicko: Why do you always do that?
Dimbo: What?
Thicko: Tag something on the end of what you say that you don’t explain.
Dimbo: Believe me, explanations are sometimes a waste of time.
Thicko: Oh, how convenient! Say something and then refuse to explain what you meant or why you said it. Now that really is a waste of time! And energy. On stuff that doesn’t even matter!
Dimbo: Okay, sorry. You didn’t pick it up, but I was being a little sarcastic by suggesting that your thinking is seriously out-of-date – like, in the dinosaur age! You can take a joke, can’t you?
Thicko: Excuse me while I die laughing.
Dimbo: You’re welcome. How long will it take?
Thicko: Ha ha ha. I can see why you’re not a stage comedian. By the way, sarcasm is the lowest form of wit.
Dimbo: Have you tested that? I mean, have you, for example, scientifically measured the levels of all forms of wit and found sarcasm to be the very lowest? Was the study peer-reviewed and approved?
Thicko: Don’t be facetious. It’s just an expression that reflects the way many people feel about sarcasm.
Dimbo: I’m not being facetious. I’m building an example-based case on an expression you chose, to show how people can accept certain things without testing them at all.
Thicko: You mean like the idea that nothing can exceed the speed of light?
Dimbo: Not at all. That has been thoroughly tested.
Thicko: How?
Dimbo: You wouldn’t understand.
Thicko: Well there you go again! Why don’t you try me, and I’ll tell you when I get stuck?
Dimbo: The problem is that if you could understand what I’m saying, you would see that I’m right, but as long as you don’t see what I’m saying you won’t understand any of it in the first place.
Thicko: That’s too complicated for me. Just tell me something and I’ll tell you if I agree or not.
Dimbo: But how will you know what to make of what I say if you don’t understand it?
Thicko: But how can I understand it if you don’t at least tell it to me? Got your new improved ESP kit yet?
Dimbo: Okay, let’s give it a go. Do you understand my light-based clock system?
Thicko: Oh, we’re back there again. Is this part of your regress-equals-progress theory?
Dimbo: Yes and no. Just give an unambiguous answer. Do you understand the light-based clock?
Thicko: Eh... no.
Dimbo: Well that’s just part of setting up the experiment so what chance is there of you understanding the results?
Thicko: That doesn’t matter.
Dimbo: It doesn’t matter that there’s no chance of you understanding the results?
Thicko: No.
Dimbo: Do you mean no or yes?
Thicko: Depends how you frame the question.
Dimbo: Right. Does it matter that you cannot understand anything about the experiment?
Thicko: Which things do you mean?
Dimbo: I said anything!
Thicko: You mean everything?
Dimbo: If you want to put it that way, okay. Let me be precise then. Does it matter that you will not understand any part of the experiment at all?
Thicko: Who says I won’t?
Dimbo: If you are incapable of understanding just the clock, the rest will be too difficult for you.
Thicko: How do you know? You didn’t even mention the rest.
Dimbo: Yes I did! Two seconds ago!
Thicko: That’s not fair. All you said was that it would be too difficult. You didn’t tell me what it was. You didn’t give me the chance to not understand it.
Dimbo: Okay. Let’s take one bit at a time. The clock on its own. Do you understand the clock? The answer has to be yes or no.
Thicko: That doesn’t matter.
Dimbo: What sort of answer is t