| From: christian | 16/02/99
22:58:20 |
| Subject: speed of light / time | post id:
1354 |
| Dr Karl, Can you please explain to me how it is that, if you travel faster than the speed of light, you can travel bacwards in time. Thankyou Christian | |
| From: Chris (Avatar) | 17/02/99
13:29:29 |
| Subject: re: speed of light / time | post id:
1380 |
Can you please explain to me how it is that, if you travel faster than the speed of light, you can travel backwards in time. Ok, this one has been coming up for a while now. Here's the strict answer. The effect you are thinking of here is due to relativity. Special relativity tells us that all inertial observers will measure the speed of light in their own reference frame as c / n where c is the constant for the speed of light and n is a property of the medium called the refractive index. In a perfect vacuum, n = 1. This postulate has a remarkable consequence, namely that different observers' measurements of distance and time depend on their motion relative to each other ! So if you hold a one metre ruler in your hands, and I fly past it at 0.9 c I will measure a different length to you! A similar effect occurs for time. Imagine you and I take identical clocks and synchronise them exactly. Now I fly away from you at 0.9 c for a while and then fly back. When I arrive back, your clock will say that a longer time has passed than my clock - because the time interval was dilated in my moving frame of reference. Naturally this effect makes people wonder what happens as you travel closer and closer to c. The answer is that the time dilates more and more, and our clocks will disagree more and more. So what happens if you actually travel faster than c? Well, firstly you can't. If you have non zero real rest mass you can't accelerate to c. However, the same math which describes the time dilation effect for us as we travel closer to c also works for velocities which are faster than c. If we solve that math, which is done by evaluating a proper time interval (squared) over a Lorentz transform (a kind of trigonometry with matrices!) then the result for the object travelling faster than light is that the proper time interval is negative with respect to a stationary observer! The interpretation of this math result is backward time travel. Now the very math that describes this effect also forbids anyone who travels at less than c from travelling above c, and also forbids anything (such as a tachyon) which travels at speeds above c from ever travelling below c. So no backward time travel for us in this way, I'm afraid! Hope this helps! Chris | |
| From: Lee | 17/02/99
15:54:38 |
| Subject: re: speed of light / time | post id:
1390 |
| Here is a theory on the speed of
light...... You are all wrong. An object can travel at the speed of light easily. If I am traveling at 99.99% the speed of light and I throw a tennis ball in the direction I am travelling the ball still has to travel away from me at the speed at which I throw it. So, to a person standing stationary as I pass and throw the ball I appear to be traveling at 99.99% the speed of light but the tennis ball is traveling at just over 100% the speed of light. Let me put it another way:- A `bug` can only fly at about 10km/h but if this bug is in a car that is traveling at 60km/h and the bug flys from the back of the car to the front of the car. To a stationary person on the side of the road the bug is flying past at 70km/h. | |
| From: Gigboy | 17/02/99
16:09:42 |
| Subject: re: speed of light / time | post id:
1391 |
| Lee, I think you've answered your own question, or at least part of it. I keep hearing the word "relativity" regarding speed of light travel, and that's exactly what you're talking about. The speed of the ball relative to a bystander and the fly relative to a bystander... Perhaps the more enlightened could expand on my ramblings... Tony. xxx | |
| From: James Richmond (Avatar) | 17/02/99
16:13:33 |
| Subject: re: speed of light / time | post id:
1392 |
| Lee, your argument sounds
sensible, but unfortunately it is wrong. The relativistic formula for adding velocities is not quite as simple as the common sense formula we normally use for speeds much less than the speed of light. Consider a person in a car with a tennis ball, and an observer on the side of the road. Let v be the velocity of the tennis ball relative to the car, u be the velocity of the car relative to the road, and w the velocity of the ball as seen by the observer on the side of the road. Now, your common sense argument says: w = v + u This works fine for speeds small in comparison to light. At higher speeds, the formula becomes: w = (v + u) / (1 + uv / c2) So, if v is 10% of the speed of light, and u is 90% of the speed of light, then instead of w being the speed of light, as you'd expect if common sense worked here, w works out to be only 91.7% the speed of light. No material object can travel faster than the speed of light. There's no getting around it (he says, preparing to be shot down in flames...) | |
| From: Jeremy | 17/02/99
16:31:28 |
| Subject: re: speed of light / time | post id:
1395 |
| Hey Lee, If you were travelling at .99c, then how can you throw a ball without it causing you to slow down (relatively)? What do you push against? You know when you swing a small object around on a string and it whacks you really hard on the head? It hurts so much because it has acquired a lot of energy. That is because you were pumping a lot of energy into the system. If you gently rest it on your noggin then it doesn't hurt, but it would hurt if it was really, really heavy for its size. So it should be obvious now that things that are travelling fast relative to another have more energy. As a massive object is made to increase in speed it acts as if it has more mass. Now - you know intuitively that it is easy (using leg power) to accelerate a bike, hard to accelerate a car, and impossible to accelerate a lorry. This is because it takes more and more energy to overcome the tendency of a massive object to keep doing what it is doing as it increases in speed. You should just be able to *feel* that this is true. It is not a linear relationship as speed increases and becomes highly significant near the speed of light. In fact, theoretically, it would take INFINITE energy to make any object of any rest mass reach c. So, if it takes more and more effort to accelerate an object the faster it is travelling, can you now see that there is a limit to how much an object can be accelerated? This limit is the speed of light in vacuum. Another concept that you will need to grasp is that of a frame of reference. This is a way of saying "From xyz's point of view". The experience of one observer is not the same as another in a different frame of reference. Let me give an example. You are travelling in a car, and ram the one in front. He was doing 100Kmph, You were doing 110 Kmph. The brick wall that you just past was stationary. If you had hit the wall, then you do so at 110Kmph, but ramming the car in front only incurs a 10Kmph hit. Same you, different frame of reference, different experience. If the brick walls were travelling at 110Kmph (same direction), then you could not hit them at all, but the car in front could back into them at 10Kmph. Different Frame of reference, different relative experience. BUT THE SYSEM IS ADEQUATELY DEFINED AND UNCHANGED in each of these F.O.R.s. Some F.O.R.s are more suitable for describing a system than others and this becomes obvious if you imagine being an observer who is, say spinning rapidly on the spot and trying to do the maths on speeding cars relative to your F.O.R. If you consider yourself to be "stationary", then these cars will be spiraling and twisting away in a complicated fashion. | |