Does the Past Still Exist?

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

One of the biggest mysteries of our existence is also one of the biggest mysteries of physics: time. We experience time as passing, with a special moment that we call “now”. Now you’re watching this video, half an hour ago you were doing something else. Whatever you did, there’s no way to change it. And what you will do in half an hour is up to you. At least that’s how we perceive time. 

But what physics tells us about time is very different from our perception. The person who figured this out was none other than Albert Einstein. I know. That guy again. Turns out he kind of knew it all. What did Einstein teach us about the past, the present, and the future? That’s what we’ll talk about today.

The topic we’re talking about today is covered in more detail in my new book “existential physics” which will be published in August. You find more info about the book at existentialphysics.com

We think about time as something that works the same for everyone and every object. If one second passes for me, one second passes for you, and one second passes for the clouds above. This makes time a universal parameter. This parameter labels how much time passes and also what we all mean by “now”.

Hermann Minkowski was the first to notice that this may not be quite right. He noticed that Maxwell’s equations of electrodynamics make much more sense if one treats time as a dimension, not as a parameter. Just like a ball doesn’t change if you rotate one direction of space into another, Maxwell’s equations don’t change if you rotate one direction of space into time.

So, Minkowski said, we just combine space with time to a 4 dimensional space-time, and then we can rotate space into time just like we can rotate two directions of space into each other. And that naturally explains why Maxwell’s equations have the symmetry they do have. It doesn’t have anything to do with electric and magnetic fields, it comes from the properties of space and time themselves.

I can’t draw a flower, let alone four dimensions, but I can just about manage two straight lines, one for time and the other for at least one dimension of space. This is called a space-time diagram. If you just stand still, then your motion in such a diagram is a straight vertical line. If you move at a constant velocity, your motion is a straight line tilted at some angle. So if you change velocity, you rotate in space-time. The maximal velocity at which you can move is the speed of light, which by convention is usually drawn at a 45-degree angle.

In space we can go forward-backward, left right, or up down. In time we can only go forward, we can’t make a u-turn, and there aren’t any driveways for awkward three-point turns either. So time is still different from space in some respect. But now that time is also a dimension, it’s clear that it’s just a label for coordinates, there’s nothing universal about it. There are many ways to put labels on a two-dimensional space because you can choose your axes as you want. The same is the case now in space-time. Once you have made time into a dimension, the labels on it don’t mean much. So what then is the time that we talk about? What does it even mean that time is a dimension? Do other dimensions exist? Supernatural ones? That could explain the strange sounds you’ve been hearing at night? No. That's a separate problem I'm afraid I can't help you with.

It was Albert Einstein who understood what this means. If we also want to understand it, we need four assumptions. The speed of light in vacuum is finite, it’s always the same, nothing can go faster than the speed of light, and all observers’ viewpoints are equally valid. This formed the basis of Einstein’s theory of Special Relativity. Oh, and also, the observers don’t have to exist. I mean, this is theoretical physics, so we’re talking about theoretical observers, basically. So, if there could be an observer with a certain viewpoint then then that viewpoint is equally valid as yours.

Who or what is an observer? Is an ant an observer? A tree? How about a dolphin? What do you need to observe to deserve being called an observer and what do you have to observe with? Believe it or not, there’s actually quite some discussion about this in the scientific literature. We’ll side-step this, erm, interesting discussion and use the word “observer” the same way that Einstein did, which is a coordinate system. You see, it’s a coordinate system that a theoretical observer might use, dolphin or otherwise. Yeah, maybe not exactly what the FBI thinks an observer is, but then if it was good enough for Einstein, it’ll be good enough for us. So Einstein’s assumption basically means any coordinate system should be as good as any other for describing physical reality.  

These four assumptions sound rather innocent at first but they have profound consequences. Let’s start with the first and third: The speed of light is finite and nothing goes faster than light. You are probably watching this video on a screen, a phone or laptop. Is the screen there now? Unless you are from the future watching this video as a hologram in your space house, I'm going to assume the answer is yes. But a physicist might point out that actually you don’t know. Because the light that’s emitted from the screen now hasn’t reached you yet. Also if you are from the future watching this as a hologram, make sure to look at me from the right. It’s my good side.

Maybe you hold the phone in your hand, but nerve signals are ridiculously slow compared to light. If you couldn’t see your hand and someone snatched your phone, it’d take several microseconds for the information that the phone is gone to even arrive in your brain. So how do you know your phone is there now?

One way to answer this question is to say, well, you don’t know, and really you don’t know that anything exists now, other than your own thoughts. I think, therefore I am, as Descartes summed it up. This isn’t wrong – I’ll come back to this later – but it’s not how normal people use the word “now”. We talk about things that happen “now” all the time, and we never worry about how long it takes for light to travel. Why can’t we just agree on some “now” and get on with it? I mean, think back to that space-time diagram. Clearly this flat line is “now”, so let’s just agree on this and move on.

Okay, but if this is to be physics rather than just a diagram you have to come up with an operational procedure to determine what we mean by “now”. You have to find a way to measure it. Einstein did just that in what he called Gedankenexperiment, a “thought experiment”.

He said, suppose you place a mirror to your right and one to your left. You and the mirrors are at fixed distance to each other, so in the space time diagram it looks like this. You send one photon left and one right, and make sure that both photons leave you at the same time. Then you wait to see whether the photons come back at the same time. If they don’t, you adjust your position until they do.

Now remember Einstein’s second assumption, the speed of light is always the same. This means if you can send photons to both mirrors and they come back at the same time, then you must be exactly in the middle between the mirrors. The final step is then to say that at exactly half the time it takes for the photons to return, you know they must be bouncing off the mirror. You could say “now” at the right moment even though the light from there hasn’t reached you yet. It looks like you’ve found a way to construct “now”.

But here’s the problem. Suppose you have a friend who flies by at some constant velocity, maybe in a space-ship. Her name is Alice, she is much cooler than you, and you have no idea why she's agreed to be friends with you. But here she is, speeding by in her space-ship left to right. As we saw earlier, in your space-time diagram, Alice moves on a tilted straight line. She does the exact same thing as you, places mirrors to both sides, sends photons and waits for them to come back, and then says when half the time has passed that’s the moment the photons hit the mirrors.

Except that this clearly isn’t right from your point of view. Because the mirrors to her right are in the direction of her flight, so the light takes longer to get there than it does to the mirrors on the left, which move towards the light. You would say that the photon which goes left clearly hits the mirror first because the mirror’s coming at it. From your perspective, she just doesn’t notice because when the photons go back to Alice, the exact opposite happens. The photon coming from left takes longer to get back, so the net effect cancels out. What Alice says happens “now” is clearly not what you think happens “now”.

For Alice on the other hand, you are the one moving relative to her. And she thinks that her notion of “now” is right and yours is wrong. So who is right? Probably Alice, you might say. Because she’s much cooler than you. She owns a spaceship, after all. Maybe. But let’s ask Einstein.

Here is where Einstein’s forth assumption comes in. The viewpoints of all observers are equally valid. So you’re both right. Or, to put it differently, the notion of “now” depends on the observer, it is “observer-dependent” as physicists say. Your “now” is not the same as my “now”. If you like technical terms, this is also called the relativity of simultaneity.

These mismatches in what different observers think happens “now” are extremely tiny in every-day life. They only become noticeable when relative velocities are close by the speed of light, so we don’t normally notice them. If you and I talk about who knocked at the door right now, we won’t misunderstand each other. If we’d zipped around with nearly the speed of light, however, referring to “now” would get very confusing.

This is pretty mind-bending already, but wait, it gets wilder. Let us have a look at the space-time diagrams again. Now let us take any two events that are not causally connected. This just means that if you wanted to send a signal from one to the other, the signal would have to go faster than light, so signaling from one to the other isn’t possible. Diagrammatically this means if you connect the two events the line has an angle less than 45 degrees to the horizontal.

The previous construction with the mirrors shows that for any two such events there is always some observer for whom those two events happen at the same time. You just have to imagine the mirrors fly through the events and the observer flies through directly in the middle. And then you adjust the velocity until the photons hit both events at the same time.

Okay, so any two causally disconnected events happen simultaneously for some observer. Now take any two events that are causally connected. Like eating too much cheese for dinner and then feeling terrible the morning after. Find some event that isn’t causally connected to either. Let’s say this event is a supernova going off in a distant galaxy. There are then always observers for whom the supernova and your cheese dinner are simultaneous, and there are observers for whom the supernova and your morning after are simultaneous.

Let’s then put all those together. If you are comfortable with saying that something, anything, exists “now” which isn’t here, then, according to Einstein’s fourth assumption, this must be the case for all observers. But if all the events that you think happen “now” exist and all other observers say the events that happen at the same time as those events, then all events exist “now”. Another way to put it is that all times exist in the same way.

This is called the “block universe”. It’s just there. It doesn’t come into being, it doesn’t change. It just sits there.

If you find that somewhat hard to accept, there is another possibility to consistently combine a notion of existence with Einstein’s Special Relativity. All that I just said came from assuming that you are willing to say something exists now even though you can’t see or experience it in any way. If you are willing to say that only things exist which are now and here, then you don’t get a block universe. But maybe that’s even more difficult to accept.

Another option is to simply invent a notion of “existence” and define it to be a particular slice in space-time for each moment in time. This is called a “slicing” but unfortunately it has nothing to do with pizza. If it had any observable consequences, that would contradict the fourth assumption Einstein made. So it’s in conflict with Special Relativity and since this theory is experimentally extremely well confirmed, this would almost certainly mean the idea is in conflict with observation. But if you just want to define a “now” that doesn’t have observable consequences, you can do that. Though I’m not sure why you would want to.

Quantum mechanics doesn’t change anything about the block universe because it’s still compatible with Special Relativity. The measurement update of the wave-function, which I talked about in this earlier video, happens faster than the speed of light. If it could be observed, you could use it to define a notion of simultaneity. But it can’t be observed, so there’s no contradiction.

Some people have argued that since quantum mechanics is indeterministic, the future can’t already exist in the block universe, and that therefore there must also be a special moment of “now” that divides the past from the future. And maybe that is so. But even if that was the case, the previous argument still applies to the past. So, yeah, it’s true. For all we currently know, the past exists the same way as the present.