## Time: What Is It?

Listening to a BBC podcast recently it seemed that the experts were agonising about the nature of time. But isn’t time just our way of describing change? Not a thing in and of itself but rather a description of real things going from one state to another?

Perhaps I’ve missed a trick somewhere along the way. If so, enlighten me.

Tags: time

My favourite definition of Time comes from a “Choose Your Own Adventure” book I read as a kid (you know, those books where there are all kinds of ways the story can end, where at various points, you choose what the characters do, turn to the corresponding page, and so on…)…

“Time, is what keeps everything from happening at once.”

-d-

That’s how we conceptualize time: we see it as just a measure of the lapse between 2 events. But according to special relativity, space and time are both intertwined as threads which make up a single fabric, where a change in one thread affects the other. The fabric is called “space-time”.

This may be simplistic, but I think about it in the same way that I think about velocity: velocity is distance over time (x/t). If we were to hold velocity constant, then making x bigger has an effect on t: it makes t bigger (if velocity is to remain constant). Conversely, making t smaller has to make x smaller (again, if velocity is to remain constant). This is easy to visualize: if velocity is constant, then it takes more time to cover more distance and less time to cover less distance.

Space (3 dimensions of “x”) and time have a relationship in which something must remain constant: that thing is “space-time”. If you move through space (x is changing over time), you experience a shorter period of time then someone who does not move through space (x is constant over time). It will appear to you that your watch ticks faster than the stationary person’s watch.

On the other hand, to the stationary person, both watches tick at the same rate, but you appear shortened in the direction of travel. In other words, if you are flying head-first like Superman, then to the person who is stationary, you appear shorter then you were before you began to travel. Note that to both people, space-time is constant. And to keep it constant, change in velocity (x/t) causes a change in t, and a change in t causes a change in x/t. In the case of a constant velocity, making x bigger makes t bigger. But in the case of space-time, making the change in x/t bigger makes the change in time smaller because velocity and time are inversely proportional.

Dale,

)

A3, I have to admit I got a bit lost on the space-time bit. I can understand the example of velocity being a ratio of distance over time and the relationship between them.

So, when I sum up time as being just another way of saying ‘change’ have I missed the mark? If we were in a universe in which nothing changed I claim that time (our concept of it) wouldn’t exist. Is that how you see it?

Also, and here comes a bit of a tangent, I have always struggled with the examples given of people playing ping pong in trains but was able to think of an example this morning which might shed some ‘light’ (ba-doom-tish) on time and the speed of light. Hear me out.

Imagine you are standing on earth and a friend of yours gets into a rocket that is able to instantly travel at the speed of light and also shines a signal back to earth as it travels. Your friend sets off on January 1 at the speed of light for another planet that is exactly one light year away. When he is half way there he shines his signal back to earth saying that he’s halfway and that it’s July 1st. The light takes half a year to get back to earth so you will receive his message at the end of December, by which time he’s actually reached his destination. On 31 December you ‘see’ him as only being half way but in reality he’s just arrived and is about to shine you another message to say so. He sends his signal along with the date and then takes off one minute later at the speed of light. One year later you receive the message that he’s reached his destination and is about to return home again. And only one minute later he arrives because he’s been travelling at the speed of light too. Both of you have been in this experiment for two years and one minute and your watches both show the same time.

Does light, space and time work like that according to Einstein? I sort of remember something about the person who is travelling fast experiencing less time pass. How does this work?

The notion of time really screws with my head especially when you start adding thermodynamics into the equation since the second law effectively defines the

directionof timeI think there is what we perceive as time and there is what physicists need time to be for everything to work. I’m sure they meet up somewhere lol.

Damian,

FYI, I just saw this on the TANSAA programme for 2009. Maybe we could carpool – if you’re interested and free on the night?

“Wed September 2, 7pm. Tim Stewart: Time and Eternity: A conversation between Theology, Biblical Studies, Literature and Physics “Full programme here

Cheers, Damian.

I don’t disagree with your summery of time at all. I was just adding that it is more than

merelya convention that we use to perceive one event as occurring before another, it is an actual part of nature in that same way that space is. As far as time existing without events, I think it does. We really have the same dilemma with space: if there are no objects, then does distance exist? I think space might exist without objects. Distance, on the other hand, I think is pure convention. It’s somehow easier for us to think that distance does not exist without a frame of reference but that space does. Unlike talking about space, the confusing thing when talking about time is that we use the same word, “time”, to mean both the lapse between events, and the part of space-time that isn’t space.To misquote Dale’s reference: “Distance is what keeps everything from being in one place.” )

Regarding speed of light travel – it works like you said… except for the time part. You will observe the traveler’s time passing more slowly – you observe Jan 1 arriving before the traveler says it arrives for him.

Just a note: nothing that has mass can actually travel the speed of light, but can only

approachthe speed of light. Theoretically, you can always get closer to the speed of light by continuing to accelerate. So the traveler, the one who shines a light toward you as he sets out near the speed of light to return home, still perceives the light moving away from him at the speed of light.A stationary observer watches you approach the speed of light, as he watches, he sees your mass approach infinity (which is why you can never actually attain the speed of light). He sees time passing more slowly for you, and sees you flatten in the direction you are traveling. From your frame of reference, time, distance, and your mass seem normal (for all we know, our galaxy is rocketing through space at near the speed of light right now – relative to some other observer, that is). If you and the observer are both traveling at constant velocities, then there’s no way to know who is really the “stationary” one. To you, traveling near the speed of light, you feel as if you are stationary and you perceive the observer as heavy, flat, and slow (I’ve been called worse).

For the traveler to return, he has to change frames of reference (he has to change his constant velocity in order to turn around and come back). It is his change in reference that makes both the observer and the traveler agree that the traveler is younger (though I’m still not clear about how the change in frame of reference does it). Up to the point where the traveler changes his frame of reference to return home, you each think of the other as younger.

Here’s the one that bothers me the most:

Experimentally, we know that light travels at the same speed regardless of frame of reference (see http://en.wikipedia.org/wiki/Michelson-Morley_experiment). Given that, consider this scenario:

A traveler traveling near the speed of light has a 1-meter rod with 2 mirrors fixed at each end of the 1-meter rod. The mirrors are perfectly aligned so that 1 photon bounces back and forth between the 2 mirrors indefinitely. The rod is perpendicular to the direction that the traveler is moving (it is “sideways” to the line of travel, like the wings of an airplane). From the traveler’s frame of reference, the photon travels 1-meter at the speed of light (299,792,458 m/s) so in one second, the photon hits the mirrors 299,792,458 times. For the traveler, the photon travels from mirror to mirror in 1/299,792.458 of a second.

We, the stationary observer, can see that indeed the photon travels at the speed of light, but the path it travels is longer than 1 meter. The reason is that the rod is moving so the photon not only has to travel 1 meter from side to side, it also travels some distance forward along the traveler’s trajectory (if it didn’t, the mirror would move forward but the photon would not so it would miss the mirror). Since the speed of light is the same for both us and the traveler, then time for the traveler must be slower than time for us since we for us, it took longer for the photon to travel from one mirror to the other (for us, the photon has the same speed but the distance it travels is greater).

So far, so good.

Now the traveler turns the apparatus (the 1-meter rod with 2 mirrors) 90 degrees to make it align with his direction of travel – instead of being aligned like the wings of an airplane as before, it is now aligned like the fuselage of an airplane. Now the electron travels back and forth along the same path that the traveler is on. For the traveler, the photon still takes 1/299,792,458 seconds to travel from one mirror to the other. But what do we see?

Let’s take the simpler case first: let’s measure the photon’s trip from the rear mirror to the front mirror. To the traveler, this still takes 1/299,792,458 seconds, same as before. Ok. We still see the traveler’s photon traveling the speed of light. But since we see the traveler shrink in the direction of his travel (Superman traveling head-first near the speed of light gets shorter), and since the 1-meter rod is along the speed of travel, then to us the rod is less than one meter. For us, the photon takes less than 1/299,792,458 to travel what to us is less than 1-meter. Earlier, when the rod was horizontal to the path of travel, we saw the photon take longer because it traveled farther. Maybe we can fix this because even though we see that the traveler’s 1-meter rod is less than on meter, we also see that as the photon is moving toward the front mirror, the front mirror moves away from the photon (because both the photon and the 1-meter rod are moving forward along the path of the traveler). So maybe the electron has to travel as far as it did when the rod was horizontal (more than 1 meter) to finally reach the front mirror. I can accept that.

Now here’s the rub. Let’s now look at the photon’s trip from the front mirror to the rear mirror. To the traveler, the photon takes the same amount of time to travel from the front mirror to the rear mirror as it takes to travel from the rear mirror to the front mirror. But for us, things are disturbingly different! For us, the photon’s trip from the front mirror to the rear mirror takes less time than the trip from the rear mirror to the front mirror did! Not only does the 1-meter rod appear to us to be shorter than 1-meter, but now the rear mirror is moving

towardthe photon as the photon moves toward the rear mirror! Not only do we and the traveler disagree on the rate at which time passes, we also disagree that the photon takes the same amount of time to go from the rear mirror to the front mirror as it does to go from the front mirror to the rear mirror.What gives??!!

Does this dependence on the direction of travel somehow explain why the traveler is younger when he returns to earth than his twin who remained on earth?

Dale, the 2nd of September is certainly booking in advance! Yes, that sounds quite interesting and I’ve marked it in my calendar so will get in contact with you again closer to the time to confirm. Cheers for that.

A3, wow, that’s pretty mind-boggling! I really like the relationship between space = distance and time = events; that makes a lot of sense to me.

If I think of the universe as being made of matter and that we take an arbitrary unit of matter to define a unit of distance (i.e. the wavelength of somethingorother) then it seems logical that we can say that the

distancebetween these two clumps of matterusing our predefined unitis 2000 units of ‘distance’. And I can do the same with time by defining a unit of time (i.e. one oscillation of a somethingorother) and say that thetimebetween event one and event twousing our predefined unitis 123 units of ‘time’.I’m thinking as I type here because I struggle with this kind of stuff so let me know if I go wrong.

The key to both ‘distance’ and ‘time’ is that they are arbitrarily defined to describe the relationship between physical objects and the relationship between physical events respectively.

With your example of the mirrors I would have instinctively thought that the photon travelling from the back to the front would have appeared to us here on earth to have taken longer than 1/299,792,458 seconds but shorter on the return journey. I’d be tempted to say that from rear to front would appear to us as taking 1/150,000,000 seconds and from front to rear as 1/600,000,000 seconds assuming the whole setup was moving away from us at the speed of light. But this isn’t correct eh? How do they verify this?

Man, this is hurting my head and I have to focus on work for a while so I’m going to continue to mull in the background and get back to this later.

Cheers, Damian.

I’ve been mulling too. It hurts so good ) )

I think you’re right about the measurements of space and time being arbitrary. Not only are they arbitrary because we define the units to be whatever is convenient, but the measurements are relative to our frame of reference: observers in 2 different frames of reference will disagree on distance between objects and will also disagree on the amount of time that passes between events… even if both observers agree on the arbitrary units.

Another thing that is a bit tricky is what we imagine when we say that the universe is made of “matter”. It’s a true statement, but the visualization I get is that the universe is made of particles – which is not quite true. The universe is made of “something”, and whatever that “something” is, it has properties of both particles and waves. One attribute of a wave is its frequency – and frequency is related to time. Other attributes of a wave are its wavelength and amplitude – and both wavelength and amplitude are related to space. Of course, particles also have dimensions which are related to space. Then all matter has a time component as much as it has a space component. Both time and space are fundamental to all matter – that is to say: both time and space are equally fundamental properties of matter.

As far as the verification of the speed of light in general, they measure the speed of light by shooting a light pulse from a laser or an LED to a mirror and timing the delay of the reflected pulse. You can also measure the collision energy of particles as they approach the speed of light in a particle accelerator, and the energy is directly related to the particle’s energy (velocity and mass). The key is that the measurements are independent of orientation. Since we know that we on Earth travel at some constant velocity, the speed/mass relationship must hold true at any constant velocity. That is, all measurements are independent of the frame of reference (see the Michelson-Morley experiment I cited above).

If we are traveling at 1/2 the speed of light, then you might think that light traveling in the same direction would seem to us to be traveling at 1/2 the speed of light. But because it appears to still be traveling at the speed of light, it must be covering twice the distance. Recall from the Michelson-Morley experiment that it’s the speed of light (distance/time) that is constant, not time or distance.

If we are traveling at 1/2 the speed of light, then you might think that light traveling in the same direction would seem to us to be traveling at 1/2 the speed of light. But because it appears to still be traveling at the speed of light, it must be covering twice the distance.Remember that the traveller’s reference frame is also apparently slowed down, so the external beam of light would still appear to travel at

. Doing relativistic speeds increases the inertial mass & induces greater curvature of spacetime.cThe part that I find amazing is that Einstein figured it all out by thought experiment (imagining himself riding on a lightbeam) — contrary to the usual scientific practice!

By the way A3; I’m still mulling but am having a lot of difficulty getting my head around it. I heard someone say that if you were on a spaceship travelling at near the speed of light and you shone a torch sideways on a wall the beam would appear directly opposite rather than at an angle approaching 45°.

But I have to confess I don’t understand why this is.

Damian, the problem might be that you are trying to “read relativity into it” when it is actually a Newtonian problem (“normal” physics problem) that can be visualized like this:

Imagine you are riding in a car at a slow, constant speed, say 100km/hr or 60mi/hr – that is, some speed so slow compared to the speed of light that any effects from relativity are so slight that they can be completely ignored.

While riding at this constant speed, you hold a ball up and then drop it onto the seat beside you. If your coordinate system is the car, the ball appears to fall straight down – there is no forward or backward motion.

However, if I am stopped at an intersection and see you do this as you drive by, I think to myself – why the hell is this guy dropping a ball in his car while he is driving though an intersection?? ) Since my coordinate system is the road and not your car, then I see the ball traveling downward, but I also see it moving in the same direction as your car. To me, the ball isn’t dropping straight down but is “traveling at some other angle”.

This is not the same as relativity though – this is just an arbitrary assignment of a coordinate system. You, the drive, can choose to measure the ball using my coordinate system in which case you see the ball moving along the direction of travel (that is, you see the road move under the ball – and if you consider the road, and not your car, to be stationary, then it is the ball that must be moving along the road). Conversely, I can choose your constant-velocity coordinate system and see the ball moving only downward with respect to the car.

The light beam you describe is exactly like the ball in the car – it is not an effect that is due to relativity. The traveling spaceship is imparting a velocity to the photon in the direction of travel (just like you, while driving, impart a forward motion to the ball).

The “relativity part” is that the overall velocity of the photon (vs some component of the velocity in a particular direction) is always the speed of light. But in your problem above, the component of the photon’s velocity in the direction of the ship is exactly equal to the velocity of the ship. So just like a rider in the car sees the ball fall straight down, the astronaut in the space ship sees the photon travel sideways.

Ahhhh! That makes sense!

Time is the distance between events like space is the distance between matter.

The thing called space-time is a useful mathematical construct, but does not necessitate the physical imposition of a real “fabric” to what is nothing.

ANALOGY: If you calculate the average number of children per couple (say, 2.4) from a sample and use that to predict a nation’s population that does not mean that somewhere out there there are real children who are only a fraction of a child.

Ah! I know the answer to this one. It is:

What is space?

Now, that, flippant thought it sounds, is the best explanation of the issue I’ve heard.