A Physics Question For Dr. Rice

Hi Dien,

The other day my 18 year old son came to me with a physics problem which I could not logically answer…..

Now I’m no physics expert, but when I was at school, I was always taught that you cannot travel faster than the speed of light.

My son posed this question to me…..

He said, “Dad, if two cars pass each other from opposite directions, and both are travelling at 100 mph…. What speed do they pass each other at?”

I answered, “Son, I believe that they pass each other at 200 mph”.

He replied, “Dad, that’s what I thought… Now let me put a hypothetical to you…. Suppose we have two space ships, and each was capable of travelling at more than half the speed of light…. And these two ships passed each other as in the car example…. Would it not be fair to say that for a brief moment in time…. Both space ships pass each other at a speed greater than the finite speed of light?
Thus for a very very brief moment in time…. The crew on board looking out the porthole would witness an object passing them at a speed greater than light itself, even though they would not physically notice it?

Dien…. How do I answer my Son?

Warmest Regards

Ricky Higgs




Sell Your Brain On The Net

It's a very good question.... which brings out some very interesting physics phenomena.... :)

Just gotta draw a few diagrams, to try to explain it as clearly as I can....

It comes under Special Relativity.... And there's a kind of Relativity in business too.... :)

Dien Rice

Hi Ricky,

Thanks for the question....

For the answer, well, what it comes down to is that, at the extremes, physics can be pretty weird.... And that's true for extremely high speeds, like speeds near the speed of light....

The Two Space-Ships....

Let's take your son's example.... Let's say we have two space-ships, the Ambler and the Blazer (or A and B for short). Let's say that both these space-ships are passing by a Space Station (or S for short) at the same time, but in opposite directions.

See the diagram below....



Let's say that a person on the Space Station measures the speeds of A and B to both be half the speed of light, but at opposite directions.

The question then becomes, what will a person on the Blazer (B) measure the speed of the Ambler (A) to be?

Normally, we would think that the answer would be half the speed of light + half the speed of light, making the answer to be the speed of light.... But that's not really the right answer.

The reason is because everyone measures the speed of light to be the same - no matter what you are doing, or how fast you are going. (This is part of Einstein's Theory of Special Relativity.)

To see this, we have to go further, and say HOW do they MEASURE the speed of the other space-ship?

What is a Light Clock?

One way to think of this is to think of a light-clock.... This is a pair of mirrors with light bouncing back and forth, each bounce is like a "tick" of the clock....

The FAR LEFT picture below shows how the light-clock on the Ambler will look to people on the Ambler, it will just be a ray of light bouncing up and down between the two mirrors....



You'll see in the top picture above (with the space-ships), the Ambler has a light clock on board. In order for the Blazer to measure how fast the Ambler is going, it can look at the light clock on board the Ambler....

Now, the MIDDLE light-clock picture above shows what the light-clock on the Ambler might look like to someone on the Space Station.... Because the Ambler is moving with respect to the Space Station, they'll see the light going at an ANGLE - not just up and down.

However, the SPEED of that light will always be a constant.... Because of that, the TIME of one click of the clock can be measured by the DISTANCE the light travels.... In the middle picture, that distance is given by t (that is, by 2 x (t/2) )....

During the time t, the person in the Space Station will see the Ambler travel the distance d (also given in the middle diagram)....

Therefore, they measure the speed to be speed1 = d / t (this just comes from the formula for velocity or speed, that if the speed is constant, then the speed is given by the distance divided by the time)....

The Answer to the Puzzle....

Now, let's look at how the Blazer sees the light-clock on the Ambler.... That's given by the diagram on the FAR RIGHT....

Because the Blazer is also going half of the speed of light with respect to the Space Station, the distance d' in the diagram is actually 2 x d.... However, the distance t' is GREATER THAN t....

Therefore, the Blazer measures the Ambler to be going at speed2 = 2 x d / t', but since t' is greater than t, this number is actually LESS THAN twice speed1....

Therefore, when you are going near the speed of light, you CANNOT just add the two speeds, to see what speed the Blazer will measure the Ambler going at.... And this is completely a consequence of the fact that the speed of light is a constant for ALL observers....

Therefore, the answer to your son's question is that the Blazer will NOT see the Ambler travelling at the speed of light, but at will instead measure it travelling at LESS THAN the speed of light....

Einstein's Theory of Special Relativity is WEIRD

In this case, Einstein's theory of Special Relativity shows that when things get close to the speed of light, our "intuitive" idea of what "should" happen breaks down....

In fact, Special Relativity has many other strange consequences, which I won't go too much into here.... Such as the slowing down of time as objects speed up, and the shortening of distances as objects speed up too....

It turns out that going near the speed of light makes things behave quite strangely! And these have been measured....

Where we can measure these effects the best are with small particles, such as in cosmic rays.... We are always being bombarded by little particles from space, but they are so tiny you don't notice it. Some of these particles have short lifetimes, before they decay and turn into other particles.... What they've found is that if these particles are travelling very fast, they live LONGER than if they are travelling slowly.... This is an effect of time SLOWING DOWN for the fast-moving particles when we look at them, compared to the slower-moving particles....

Relativity has a Place in Marketing Too

There is a kind of RELATIVITY in various aspects of business too....

For example, take bundling and pricing. On TV, you may sometimes see people selling a SET of things bundled together - such as knives, for example. In fact, in some cases the price of the bundled set could actually be MORE than if you bought all the pieces separately! In this case, addition doesn't really hold.... However, here, adding the prices turns out to be LESS than people's perception of the value of the bundled set....

Another example from sales comes from simply how people's mind works. They've found that if a salesperson shows you an EXPENSIVE item first, then shows you a MIDDLE-PRICED item, you'll perceive the middle-priced item to be cheaper than if they first showed you a CHEAP item. It's all relative, as they say!

And another example of how this is often used in marketing online is if people want to sell their "manual" at a high price -- such as for a few hundred dollars. Of course, then they DON'T compare the price to your average $20 book -- instead they'll compare the price to a $1000 seminar. Again, it's relative, and they lead the person's mind to thinking it's a bargain by using a technique of relative comparisons....

Thanks for the question, Ricky.... I had to do some thinking to think how to explain this in a way without using much mathematics.... If you'd like a more mathematical explanation, look up "special relativity" and "addition of velocities" on a search engine (you'll probably find web pages that talk about Lorentz transformations etc.)

That's this week's physics lesson from Dr. Dien! :)

Hi Dien,

Thank you very much for taking all that time of yours to prepare that detailed answer. I knew I would get a easy to understand answer from a well respected quantum physicist that you are.

I've printed it out and given it to my son... Although I must admit I had to reread it several times to understand it all!.... Now I know why I stuck to marketing instead of physics.... I'm not smart enough for all that rocket science stuff!

Dien, you are right about there being "relativity" in business and in life itself.

Everything is relative to where you stand, and how you perceive things in your own mind.

For example, (and being a fellow Victorian, you'll understand this)... When I sold my first house in Mt Waverley and moved to Bayswater, my mother said, "Ricky...That's so far out!". I said to her, "Mum... Far from what?"... If you work in the city, yes it is further to travel than Mt. Waverley... But if you work and shop in Knox and rarely visit the city... Then it's not far out of town". My mothers perception of distance was based on a certain radius from the heart of Melbourne, where mine was based on where I worked and played.

In sales, pricing is also relative and takes on a whole new perspective depending on how you state it. For example, I often used the "reduction to the ridiculus close" when selling high ticket items. A $6000 air conditioning system sounds a lot cheaper if you tell them, "it will only cost you $5 a day, the cost of a couple of bottles of beer, for the comfort of your whole family".... Now is the happiness of your family worth $5 a day?"

Yet, in reality, that $5 a day (on finance) over 5 years at 10% interest ends up costing them $9000 all up!

Warmest Regards

Ricky Higgs




Sell Your Brain On The Net

Dien, thanks for that very detailed explanation.
> Thank you very much for taking all that time
> of yours to prepare that detailed answer. I
> knew I would get a easy to understand answer
> from a well respected quantum physicist that
> you are.

But Ricky, I'm curious to know, exactly which part was 'easy to understand?' (just joking) I'm still trying to get past the first paragraph. :-)

Best regards,

Eliz.